If the door is closed then he gets total cover and total concealment. It is possible to do enough damage that your arrow goes through the door and may still hit him, though it is highly unlikely.
If the door is open then it is divided based upon a question. Is the character trying to take some kind of cover from the doorway?
If yes then he gets at least partial cover (+2) and maybe as much as near total cover (+8) depending upon descriptions and cirumstances.. If no then he gets nothing.
If two guys are sixty feet apart, shooting each other with arrows, and there is an open door in the middle between them then neither one gets any cover. They have line of sight and are angled so that they have the best possible angle (i.e. no cover) to the other guy; and the other guy has the best possible angle to them.
