This curtain rod is very effective to insulate doors. I wish I could find it in the US.
It opens and closes with the door. However, when you close the door, a special feature causes the curtain to cling to the wall, blocking any cold air on 4 edges of the door and on the surface of the door.
It also can be attractive since the whole hardware, door edges and door hinges are hidden by the curtain.
I've seen it in French homes for 30 years (approx. $30). I am surprised every American house doesn't use them.
See pictures on this French site: http://www.leroymerlin.fr/v3/p/produits/kit-de-tringle-a-rideau-met...