Plane that always flies into the wind?

Wind is nothing more than the motion of the ground relative to the airmass. A plane flies within the airmass and has no way to "know" which direction the ground far below is moving. So, no, what you propose would generally not be possible. Exotic schemes based on operations within the wind gradient, albatross-style, could be an exception-- arguably in this case an aircraft does "feel" the wind and there may be some way to harness this effect to drive a direction-pointing tendency. But certainly not if the aircraft is flying within a uniform airmass that is translating horizontally at a steady rate with respect to the ground.

If the glider is dropped from a high platform that is anchored to the ground, then immediately after it is released its ground speed will be zero and its airspeed will equal the windspeed and it will certainly tend to yaw or "weathervane" to point directly into the wind, but if it has dihedral, it will also tend to roll in the direction that sets the glider up for a banked turn away from the wind direction. So if we want to design the glider to yaw into the wind immediately after it is dropped, it should have a large vertical fin, minimal rotational inertia in the yaw axis, lots of mass in relation to total surface area, and a mid-wing configuration with no dihedral. But these characteristics will only produce a temporary tendency for the glider to yaw into the wind, immediately after being dropped. Eventually the heading will inevitably wander to point in some other direction.

TLDR

We're going to have to break down your requirements and define them to be able to answer:

Plane

so, a heavier than air craft that uses lift to defy gravity

flies

so, "remains aloft for a period of time". What period is acceptable to constitute flight? I'd say indefinite, because you said "always" but..

into the wind

so, capable of moving away from a reference point that the wind blows towards

uncontrolled,

so, either has no controllable surfaces or no device (pilot, autopilot) capable of controlling the surfaces

dummy

so, no innately intelligent/adaptive ability to respond to changing conditions

glider

so, not powered by an engine type device providing constant propulsion

dropped

so, not provided with any initial horizontal inertia to achieve airflow over its lift surfaces

face into the wind by design

so, having an asymmetrical aspect that will rotate it around its balance point while that aspect is experiencing a force from the wind

Would it be possible?

The requirements are likely to be in conflict depending on how you define flight, but if you start high enough and trim your plane well enough, and don't provide starting conditions that are too hard to recover from you might achieve something you define as a plane flying into wind before it hits the ground. The craft could be placed into an airstream above a reference point, and would initially fall as well as being blown away from the reference point. As gravity accelerates it, it could achieve a flight path such that it turns and starts moving towards the reference point again and possibly move past it to end up upwind of it by the time it hits the ground. It would take longer to hit the ground than a free falling object.

Would this be flight?

What would it look like

You've kinda specified already that it has to look like a plane. It wouldn't look exceptionally different to any typical plane you could imagine

The ? version:

Are we designing it right now? It might be better to get a handle on the physics involved first..

If we start off with a simple device that turns itself to face the wind, maybe it would look like a windsock. A windsock works really only works because it is anchored to a pole that is anchored to the ground. When the wind blows on it, it experiences wind of some speed relative to the fact that it is fixed in place. The windsock extends in the direction that the wind is blowing and remains thus because the pole is constantly providing a force that keeps the sock stationary, thus it constantly experiences a force from the wind. It is light yet presents a shape that experiences a large amount of friction on the air rushing past it. The air drags it out into a windsock shape

Imagine if the windsock tore loose and blew away. This drag would cause it to quickly accelerate to the same speed as the wind. If the wind were perfectly turbulence free it would retain its shape because it is now an object doing 60 km/h in an airstream also doing 60 km/h but it would fall to ground (and end up looking not like a windsock) because it has no way of defying gravity. If it experienced turbulence it would get kncocked out of shape before it hit the ground. But the idea was there - it's something that can catch the wind and turn to face it.

Let's dispense with the problem of gravity making our stuff crash and talk about something buoyant instead, like a hot air balloon. It resists gravity because of the hot air and starts moving in some direction because the wind is blowing against it, pushing it. Eventually, let us suppose the balloon reaches 60km/h because it's part of an airstream doing 60km/h. It's no longer experiencing any forces that will turn it around or accelerate it because it's doing the same speed as the only thing that as pushing on it; the 60km/h wind

Suppose you really want to turn your craft and you have had some huge paddle on a long pole. Normally it's stashed carefully away in the basket of the ballon, but during flight you assemble it and it ends up looking like an enormous lollipop, and you and stick it out of the balloon sideways, flat side of this massive lollipop turned so it's "catching the wind" rather than "slicing the wind" (lollipop face vertical, not horizontal). Sideways as in, if the balloon is heading East, the lollipop is pointing North or South

If the balloon is already doing 60km/h and the lollipop is doing 60km/h and the wind is doing 60km/h, will the lollipop experience a force that (if it were bolted securely to the balloon basket) will cause the balloon to rotate (so that the lollipop is downwind of the balloon) ?

No ... Because everything is doing 60km/h already. The wind doesn't blow any harder on the lollipop than it does on the balloon. There is no overall force acting on anything in this setup

Suppose you could turn the wind from "blow" to "to suck", like on a vacuum cleaner, at the flick of a switch so that it abruptly reverses direction. Now there is a force acting on the balloon and the lollipop. The balloon is going east at 60km/h, the wind is suddenly blowing towards the west at 60km/h.

The shape of baloon plus lollipop is asymmetric, so the lollipop is catching the wind on one side and there is no lollipop on the other side to balance out the forces.. So the asymmetry of the lollipop will make the balloon rotate so the lollipop is downwind of the balloon.. Why downwind? Because eventually the balloon will rotate to a point where the lollipop is slicing the wind; the wind is blowing towards the East, the lollipop is pointing towards the East. There isn't any part of the lollipop's face that the wind is blowing on, so it experiences no overall force. Because of inertia the balloon will carry on rotating so the wind is blowing on the lollipop again, this time on the other side. The effect would be to stop it rotating clockwise, and starting it rotating counterclockwise. It will oscillate back and forth in its rotation, and each time it won't rotate quite as far thanks to friction (drag) experienced by the object as a whole.

It might even become stable (stop rotating, because the "into wind" part of the question implies that the direction the craft points be fixed relative to the wind direction) but we need to hope that the balloon finishes its oscillating before this opposing wind manages to slow the whole thing down from 60km/h (going East, say) to 0 and then accelerate it up to 60km/h in the opposite direction (going West, say). If it doesn't manage to stop the balloon's oscillating rotation by the time the wind blows the whole thing so it's doing 60km/h then the entire assembly will stay rotating slowly around forever because we're back to that situation of averything doing 60km/h and there being no overall force

If you think about it, most things that fly with direction are like this balloon and lollipop arrangement - helicopters, planes, ships, windsocks. That "thing sticking out to provide asymmetry so a force can be appllied to the end of it to turn us around" could be applied to your uncontrolled glider too, but I think you really need to consider what you mean by uncontrolled.

If, like early humans did, we move on from the balloon as a gravity defying device and try and devise a plane shaped thing that meets our requirements, we will probably end up with something shaped a lot like a modern plane. There is a huge variety of shapes but when you look at them from various angles there are some aspects that are symmetrical and some that are not. We generally design them so that when viewed from the top they're symmetrical with respect to the direction they're supposed to fly in, which helps provide some symmetry to the control for rotating them and also helps them achieve a low effort stable and level flight. Viewed from the side there is an asymmetry that generally helps with both the overall design goals of defying gravity and turning the plane round so it flies in the direction it was designed to. This does all mean that they're engineered to fly well in a particular direction and orientation. Some can fly in other orientations, for example you might be able to balance things out so a plane flies "on its side" and the air smacking into the side of the fuselage keeps it aloft and defying gravity, while the rudder keeps it turned so that the fuselage is always making a suitable angle for the air to smack into and the engines keep pushing it forward fast enough to keep the air smacking the fuselage but it doesn't need considerable amounts of control and power to fly this way

You've set out that it's a glider so doesn't have any power of its own, and it's not even clear whether it gets an initial push in the sight direction because you're just "dropping" it into an airstream, which I take to mean that you're going to throw it out of the back of a larger moving plane, possibly the same speed backwards as the larger plane is moving forwards so that initially your glider has no velocity. It has some unspecified attitude (angle/orientation) that isn't necessarily its stable, level flight configuration (and for the most part probably won't be - I'm assuming you'll want to test how your glider performs in recovering itself when you start it off from an orientation that is unusual. I'll also assume that you're out are so good at throwing it that it has no initial rotations

Gravity affects things significantly right from the start. The wind might or might not affect things much depending on the craft's orientation. There will be some part of the airframe that is catching the wind and will experience a force. If it's in a stable level flight orientation, that force isn't huge because we try and design things so that it isn't, giving us less friction to overcome (costs less to run an engine, flies for longer on its own inertia), but it's present. Absent any other factors the wind will be blowing over the lift surfaces giving it some ability to resist gravity, but it will dip towards the earth because trimming for stable level flight needs the craft to have some consistency to its speed and it's speed is already changing. Over time things will try to balance out; various factors about the asymmetry of rudder and elevator conspire to turn the craft around so it points towards the direction the wind blows from but the only way it can fly into the wind is to use gravity to overcome the friction the frame experiences from the wind blowing on it, and gravity is in finite supply because altitude is in finite supply; you can't make this craft fly indefinitely so you could say you can only design it to resist crashing as long as possible. It will probably have adopted a flight configuration that means it's pointing into the wind by the time it crashes though

If you make things really hard, give a large amount of rotation in all 3 axes to your magical shaped thing when you throw it out of the hatch of your B52, then there is a good chance that it will never work out; the asymmetry of the rudder and elevator will try their best to reverse some rotation that is going on but there will need to be friction to reduce the oscillations. If you increase the friction you increase the wind's ability to accelerate the airframe. Even if you keep friction low, in this crazily rotating mode the craft will spend a large amount of its time facing in a direction where the wind can push directly on all the surfaces of the craft, particularly the wings and fuselage meaning that the craft quickly accelerates to the speed of the wind and that then means it's just an object free falling under gravity. As it accelerates it picks up speed that may improve the wings' ability to provide lift if the craft is oriented so that they're in a flying direction but overall your glider is really heading in the wrong direction and self recovery to something that could be called flight is unlikely, so even though the rotation is constantly changing you'll probably see it tumbling over and over until it crashes. Deploying a big windsock out of the back end for a while until the oscillations stop, then cutting it loose might work out - but that's getting back to having active control of the craft..

Balloons defy gravity because they're buoyant, planes and gliders defy gravity because they maintain some relative difference in airspeed over their lift-providing surfaces. If you're looking to design something that remains aloft and weather vanes (turns to align itself with the wind direction) I recommend you first find a way for your device to remain aloft and adopt a stable flight (maintains altitude without tumbling around) - this reduces the number of problems you have to solve in terms of 3D movement. Then resolve this problem of it needing to turn into the wind and cease its rotating oscillation sooner than it accelerates to the point that it's doing the same speed as the wind.

It will probably be like a hot air balloon with a light part at the top and a heavy part at the bottom. It will be very heavy so it has inertia but the weight will be very close to its centre of rotation, so a rudder (lollipop) type thing can easily turn it (low rotational inertia) but it is hard to blow it sideways (high lateral inertia). It will have a symmetry to its body and buoyant enough to counteract the core weight.

That does leave us with the problem that you called for not only pointing into wind but flying into wind. No matter what you design, even though it might be able to point into the wind it won't be able to fly into the wind, "flying" defined as "remain aloft indefinitely". An unpowered balloon can't fly into the wind at all. A glider can only fly into the wind while gravity overcomes the friction caused by flight and we know that gliders don't remain aloft indefinitely without some external driving force because the friction they encounter reduces the inertia they need to keep flying or gradually gives them an inertia that leaves them with no airflow to generate the lift needed to keep flying. A propelled plane flies into wind because the engine provides the power to overcome the friction, but only for so long as the engine runs.

This means that the answer to your question as presented, is probably "no", based on what I guess you want

Do you have to have information about the ground? No!

Ground tracking is far too expensive. A simple gyroscope that is set just before the drop will do the trick. Search online for miniature gyroscope for model planes (if indeed it is for a model)

Otherwise buy yourself a quadcopter and steal the appropriate bits out of that.

The answer is no for an "uncontrolled dummy glider".

To explain, I am going to make a few assumptions that aren't stated in your question: The glider is inherently stable on all axes, it is dropped from a balloon that is drifting with the wind, and the air mass is uniform and stable.

In this case a dummy glider will have no sense of any wind. Only the person releasing it, and/or a GPS system would realize that there is a track across the ground. The glider will glide forward through the airmass, (that it is already moving with...) in whatever direction it is pointing when released.

Air is only called "wind" when it is moving relative to the earth. The reason a kite or simple weathervane points into the wind is because they are fixed to the earth's frame of reference. A free glider isn't.

suppose you dropped an uncontrolled dummy glider into the air...

Dropped is the key word. Upon release the glider, if it were directionally stable, should "point" into the "wind". The key is the definition of relative wind. This would be air flow relative to the air craft. Any heavier than air craft must have some relative wind to glide.

A glider creates lift by making its own "relative wind" by converting mass and altitude into airspeed. However, when it is first "dropped", it only has the force of wind relative to its drop point on it. A gravity bomb dropped into the slipstream has fins to help it "point" forwards. An aircraft parked on the tarmac will try to point into the wind, but the friction from its tire prevents it from doing so. But the common weathervane uses its "tail" to always point into the wind.

So once the plane is moving, the direction it "points" will be in the direction of its "relative wind", which is a combination of its forward motion and any side force winds.

Side force winds will accelerate the plane in that direction, and then and only then, does the plane "not know or care" about wind direction (relative to the ground). The danger of microburst gusts makes this point abundantly clear. (There is an opposite effect once the gust passes).

what will this plane look like?

Any aircraft with directional stability

"Uncontrolled" is a bit vague. I am assuming you are referring to wind as measured in the reference frame of the ground. To face the wind, the glider needs to know where the ground is located at a minimum. A simple example would be a kite, where the only control is a connection to the ground. A good kite always faces into the wind.

If you are referring to wind as measured by the glider, all gliders in normal operation fly into the relative wind.