One thing for sure is that the weather does not change once you've committed to battle on a given day. The AI once again besieged a city of mine where I had a clear numerical and qualitative advantage over the sieging troops. I sortied out to meet them and it was raining. Since I had 5 Roman archer units which are useless in wet weather I hit Ctrl-T to speed up the time and hoped for clear skies, just like I used to do in Medieval... no dice. I left the time compression on for a looong time and the rain never let up. So I stayed inside the city walls, ended the battle in a draw and then sortied out again, this time under a sunny sky.