You may need to move the strike plate closer to the door stop to get the play out of the door.
If there is good weather stripping around the door stop,move the strike plate.If there is no weather stripping or old worn out stripping replace it first,then if need be adjust the strike.
To adjust the strike,close the door then pull it towards you tight against the strike,mark on the jamb where the door is,then turn the knob to open the door but push the door snugly against the weather strip,mark on the jamb where the door is now.This is how much you need to move the strike plate.You need to remove the strike plate and fill the screw holes. I redrill these holes to a 1/4" and fill with dollrod and glue,but in a pinch any sliver of wood that fits over tight and glue will work.Move the strike to the new spot,mark and drill new holes,reattach strike and see if this doesn't fix your drafts.
You may also need weather strip or sweep on the bottom of the door.Luck