I was playing the D.E. tonight, and one of the A.I. characters used two bows in a single combat. Since the bow is not classified as a weapon, this is legal.
It's kind of like using two Warhorses. Nothing prohibits it, but it seems to go against the logical possibilities within a combat. You can't ride two Warhorses into combat. Neither can you fire two bows.
The bow should be classified as a weapon, but one that permits you to use one additional non-bow weapon in the combat itself. (The Warrior would then be able to use the bow plus his regular two non-bow weapons.)
It would appear that the purpose of not classifying it as a weapon would be to permit the bow to be used in addition to another weapon.
Either way, be on the lookout for using extra bows. It can be done.