I think it would be better if the rain severly affects the "cruder" bowmen. Elven, and to an extent, human bows I presume would be a light but strong material, however Orc bowmen would probably use rope. In that case Orc bowmen (or goblin) should shoot not as far and accuracy much less.
Agreed. That would add to the realism.
"Do not come between a Nazgul and his prey..."