I don't know of course, because I wasn't there, but I suspect it's a misconception that everyone went about wearing armor in the middle ages. English warbows were extremely heavy because they were made to bring down armored, French cavalry. But the majority of most armies would have been made up of commoners with spears and no metal armor. So your "knock about hunting bow" actually could have been extremely effective raining bolts down on the cannon fodder trying to cross the moat or border reivers trying to pound down the gates.
Effective, that is, up until the archer accidentally dropped it off the wall into the moat. I wonder what the cuss words were in old English? "Alas, 'tis #@*!!!"