I'll try to be the more specific possible but please consider I usually talk French.
I'm not the owner of the place I live, I'm renting it. So something like changing a door is not something I considier that I should change if something goes bad with it. Especially when one of the main prupose of a door is not meet; stopping cold air from coming in. But the owner don't want to change it (waste of time talking with him anyway ; "Costs too much." he'll say - I literally hear him saying it).
So I was wondering how could I fix the fact that yes, my exterior door is closing correctly, but there's a huge and quite considerable amount of air entering by where the metalic piece from my door went into the wall hole.
Note: It's not my door, it's an example. Mine have a door lock about 2 inches over the handle.