Does aluminium foil still reflect heat if covered?

As Broken Admin mentioned, its better to think of the foil as reflecting heat rather than reflecting cold. Its not that it reflects the cold from outside to keep it outside, its that it reflects the heat from inside.

Metalized foils like these reflect infrared radiation. Every object emits it. The hotter the object, the more it emits. If you have a really hot object, like 800 degrees hot, it can even glow in the visible range. But even if its colder, it's emitting in the infra-red range.

The idea is that, without the foil, every surface in your house is emitting and receiving a bunch of infrared radiation based on its temperature. Mostly its in balance, but some of that radiation reaches the window and escapes into the cold outside. If you put foil in place, it instead reflects the heat back into the house to get re-absorbed by the floor/walls/etc.

This foil is more effective than, say, painting the windows, because that surface also has conduction to deal with. The windows are simply colder than the rest of the house. Perhaps not quite as cold as the outside world, but cold. So painting them would help a little, but you'd still have a cold square that wasn't radiating quite as much. Foil reflects the radiation rather than absorbing it, so the temperature of the foil isn't nearly as important as it was in the case of painting the window.

So with the shutters and curtains, the foil still works. Why? Because the shutters and curtains are still quite warm, being fully inside the house. They are radiating, and losing heat through the window. A layer of foil reflects that heat, letting the shutters or curtains reabsorb the heat.

What you shouldn't do is have the shutters or curtains plastered against the foil. In that case, the infrared radiation would play a smaller part because conduction directly through the window, foil, and into the shutters/curtains would dominate. But as long as there's a nice insulating air layer between them, it will do the job.

I'm unsure what exactly you are describing, but from what I understand $-$ you plan to "reflect" heat from outside the window away from the room. I'll attempt to explain a basic idea.

Closing the curtains and shutters would prevent some heat from entering, but heat which makes it past the curtains and shutters will be reflected away from the room.

The foil on the in-facing side will not reflect "cold", as cold is just the absence of heat. But it will reflect any existing heat from exiting the room.

If I misunderstood your question, please comment, as I'd be happy to provide a more accurate explanation.