i think weight is on your side. it seems that you would want it to hang as close as possible to the door (like double glazed windows) as you can and still let the cat in and out. i would even put weighted chain the bottom for that purpose. during the day, or in warm weather, swag it back to a decorative hook. and i would hang it high, to keep out as much draft as possible. remember that heat rises (you don't want to lose that) and cold falls (right around your feet). i would hang it smack against the wall with a quilt hanger, pinch or dowel type, no gathers to create tunnels for the air to move around in.
your only concern will be outside light coming through the glass. it may fade the quilt and the batting and backing will not protect it.