maybe take the door(s) off the closet stashing them to the inside of the closet out of the way and then hang a sheer curtain on a spring rod in the door way.
The sheer will allow light in from the window in the room giving natural day light hours.
You would be surprised how well a sheer will hold heat in an area.
I do that in my snake room vs the rest of the house to help hold extra heat in there during the winter. I keep my house at 65 during the winter with an electric heater in the snake room keeping it a balmy 80. Works Great.