Do it the 'real' way. There are black plastic bristle brush things that are meant to prevent drafts under doors while still allowing entry- they may be permanently installed with no damage to frame, door, floor, woodwork, etc.
I don't know where you live, but up here where it's cold and a high number of the houses are over a hundred years old (=drafty), everyone has 'draft snakes' that you just push up against the edge of the door when you close it. All it is is a leg from a pair of knitted tights- thick ones- filled with dry beans and tied shut. Works like a charm.
For the other 3 sides of the door, install weatherstripping on the door frame if light comes through.