in tbb (dont remember which one) I think it's john strunk that mentions that in the days when bowyers used hide glus to splice billets it was not rare to see archers going to their car after a day at the target butts with two half bows under their arm. They would glue them back up when they got home. Although it can be done with hide glue, I recommend using a weatherproof wood glue (tite bond 2, tb 3, Urac, Epoxy, etc) for a more permanent bond.
hope this helps