I'm willing to believe that there will be a cladding, possibly a PVC panel, possible cement board or something, on the outside. There is probably a cavity between the inner and outer skin which is probably filled with expanded foam, which is a good insulator. It might be that chilled air is waterfalling down the glass window and cascading over the inner PVC skin.
If the build is rather old, there is a chance that there is no insulation in it.
Your long curains would be a good solution.
If there is no insulation between the skins, it may be possible to add it from the inside, but it might involve cutting out the existing panel. Don't try to inject expanding foam, because this is one of the cases where the expansion would push the faces apart in a big bulge, and possibly push them off the wall or break them.
If you have draughts round the edges where the frame meets the wall, this can be cured with expanding foam into the crack, finished off with white silicone. You need a very careful workperson who is experienced, since expanding foam is very sticky and will ruin decorations, carpets, clothes, hair, skin or eyeballs if it touches them.
You might be able to have a panel of insulated plasterboard fixed over the inner surface, about two inches thick, the plasterboard face can be painted or papered like a wall.