Many games that have weather effects use them merely for atmospheric purposes: it may be raining, but it has no effect on the world in general. NPCs will still wear the same clothes as before, the ground is as dry as before, flowers cast the same crisp shadows as before, ... M&B is different, though — when it rains, it affects missile use. Because I get shoved off ladders by my own troops, I usually end up sniping with my crossbow during sieges, so when it's raining that's bad news. Still, it'sa degree of realism more than most games have.
Of course, it's not so real as to ensure that the rain isn't pelting down in the middle of a desert.