If there is a big draft coming into the rental through the door frame, the best way to fix it is to go down to the hardware store and get some weather stripping to place in the door frame. Either you can ask the landlord to pay for the weather stripping and if he or she refuses, you should do so to get the problem resolved.The cost of the weather stripping should not be that much in my opinion, less than $50.00 or so.Another option is to have the property manager to fix the door with weather stripping.