Cold air return? or not?

We have a small bungalow house, at one time a small addition was put on the back (10 x 18) there is one heat vent in that area (center of long wall on outside wall), no cold air return. then entrance to this area is along one end opening of about 6'), through ther kitchen. The problem seems to be in the cold weather there is a draft along the floor of the kitchen coming from the added room, should I add a cold air return in there, or would it just be defeating the purpose of the heat vent that is in there? thanx.

 

If you push air in there, something has to come out! I'd add a return duct...