Can/Should I use an angle grinder with a blade for metals on PVC coated metal?

I think you'd do better with a Sawzall. That's the trade name - like Kleenex, everyone uses the name no matter what the brand. Just looked up - it is generically a reciprocating saw. These things can be dangerous beasts, but I think they'd be a lot safer for this type of job than an angle grinder. Buy/beg/borrow/rent - for one small job, any of the options will work. Just make sure you have a blade designed for cutting metal (very hard material, closely spaced teeth) and not wood (wide teeth). Corded or cordless.

Using an angle grinder you're going to end up with melted PVC clogging the blade, and possible fire from hot metal/sparks that you are grinding igniting the plastic, etc.

As such, the suggestion to use a reciprocating saw (effectively a form of power hacksaw) is valid - however, since you already own a hacksaw, and it does not seem like it should be such a huge job, I would suggest that possibly your hacksaw blade might be dull, if it's "doing nothing to the steel" and that a new, sharp, hacksaw blade might be a very different experience. Hacksaws are made to cut steel, but a dull blade won't cut much of anything. Hacksaw blades are replaceable precisely so that you can have a sharp one easily (they are not generally considered to be practical to sharpen.)

Yes, it'll be fine but heed the valid warnings given in the other answers about the minor risk of melting plastic and starting small fires. You won't instantly be sitting in the middle of a blazing inferno; it'd me more like having a few birthday candles in front of you, but the fumes are unpleasant.. The biggest risk from an angle grinder in this context is probably from the tool itself

To reduce the amount of melted plastic, don't hold the grider in the same place; go back and forth across the plastic so you aren't overheating any one part causing it to melt. Have a damp cloth or water sprayer on hand to smother anything that ignites. PVC frames that are reinforced have metal box section inside that is a snug fit, so you're unlikely to start a fire inside the frame/any flames you see will be surface only. Additionally, you seem to have already removed the frame from the building so cutting it up in the yard is considerably safer than generating a sparkshow with it still attached to your house, and if you can arrange for good ventilation and a mask to avoid inhaling fine particles it will help.

If you're not into all this doom-talk of fires and would prefer to avoid the possibility you'll probably have good success in using the hacksaw to cut along the plastic weld lines. In my experience the fabrication of PVC units is that long straight sections of profile, including a metal box section, are cut to length and then only the plastic is welded; the metal isn't welded/doesn't continue around the corner. The metal just provides bending resistance for the mid section. If you do find metal in the corners, you may also have success in cutting the plastic all the way round in some part of the mod section, then smacking the frame apart with a hammer - the box section isn't fixed to the plastic (except for where you've screwed frame fixing through it) so they should separate with some determination

As the goal is just to make it smaller:

I'd use a sledge hammer to fold it up until it fits in the car, or if there's room just store it (even outdoors) until the next council hard waste collection.

FWIW, I had a similar problem with some steel re-enforced concrete. I used a stone blade to cut away a load of the concrete, exposing a reasonably large amount of the steel, then switched to a metal blade to cut the steel. I did try a (new) hacksaw, but found it tedious, and seemed to dull the blade very quickly whilst doing relatively little to the steel.

In this case, I'd say use the hacksaw to cut away a chunk of the plastic/wood and then grind through the steel - but take suitable precautions to avoid sparks on the plastic or plastic on the grinder. Avoiding heat is probably the best advice, so moving the grinder about so that you're grinding different bits of metal at a time, and maybe just go at it for a couple of minutes, then leave it for 10 minutes before you go back and do a bit more.

Another answer recommends a sledge hammer. You may find that when stripped of the plastic and wood, the steel buckles and bends more easily than you might imagine (when suitably persuaded by a hammer). The problem is that's a one-way trip. If you start doing it that way, you're going to have to finish. At least with the grinder you could change your mind and switch to a different method.

The last thing I'll just add is that our family car has some Tardis-like qualities when it really needs to (ie. when I've bought a load of materials without thinking about how I'm going to get them home). You may find you can fit more in your car than you imagine if you try hard enough, so may need a lot less cutting than it may appear.

A circular saw with a common carbide-tipped blade will make quick work of it. The steel in such frames is soft and will dull your blade only slightly, if at all.

Otherwise, just knock it apart at the corners and slide it into the car. I carry 8' lumber in my little sedan all the time.

Use eye and ear protection.