Not an RPG guy, but you've got crossbows right. As regards longbows (if they're in a game) I'd expect there's no consideration of weather. Like early (non-percussion-cap) black powder, their effectiveness is in inverse proportion to the amount of rain.

Might be the same for crossbows, although the historical ones I've had a chance to look at (Higgins Armory, sadly now gone) seemed to use either metal (probably early spring steel) or horn for the arms of the bow, and there was proportionately less 'string' (gut strings getting wet being the nemesis of the longbow). The one with a foot loop and windlass appeared to have a string made of some kind of metal, but that was in a glass case (and I'm pretty respectful of not touching anyway as I know how skin oil can damage things)

When I went to school in Normandy, I got to tour a couple of castles in the area contested by the English. No signage, but a couple of the thick oaken doors had what appeared to be random through dowels which I took to be evidence that some kind of arrow or wooden bolt had passed through and lodged, been cut off, sanded down. Henry V? Longbows? No idea, but maybe...