The short answer, most likely. As for insulation, you could replace the trim weatherstripping, or just use a 3m or Frost King plastic vapor barrier kit, to seal from any air transfer, until you fix it when you can.
It would be good if we could see the doors. I have a similar problem in my office at work. when the section of the building I work in was remodeled they put in new windows. The thermopane glass is real nice but, the aluminum frames are horrible. Simple extruded frames with no insulation or thermal break. On a cold night, I can set a water bottle on the frame and in the morning it will be slushy to almost frozen.