There are several thing you can do to minimize the draft comming through your door.
First off don't take the door off yet. Make sure all the screws are tight on all the hinges. Once thats done look for the gaps around your door.
Now say there's a gap on door knob side top or bottom put a small shim (piece of carboard) between door jam and hinge that is across from largest gap, most cases this will work. Same if gap is at top door knob side put shim on lower hinge.
If you have a gap on the bottom you may want to try a door sweep, there are many types and its hard to say unless I get more details of door bottom. You may also need a new threshold that could be bit tricky to match up and install. The foam stripping will help. Contacting the manager may get results as well. Good luck.
BTW I've 22 years exp. in DIY and that is what I do for a living facilities maintenance.