Closets against an exterior wall will get cold. It doesn't matter much how much insulation is in the wall. When you close the closet door, you cut off warm air circulation in the closet. The closet will cool down simply because it doesn't have a source of heat, and as the closet cools down, the exterior wall in the back of the closet will feel (and actually be) colder than the exterior walls in the room.

As for the bay window. Lots of glass, low R value, even the best windows only have about an R-3 or so. Warm room air is going to hit the glass, cool down, get heavier than the rest of the room air so it sinks to the floor. If you put your hand near the glass at the bottom of the window, it can feel like cold water flowing over your hand. That will make the seat and the floor colder.