The manual does not explain much about the weather and the Wiki echoes this. The CW2 DB only indicates that the weather varies by what appears to be altitude, so no mention of the game mechanic. I checked a log of a battle that lasted 3 rounds and there is no mention of the weather at all. The in-game battle report picture menu can be reviewed by round/day. I'll make it a point to see if the weather on the menu ever changes.
I'm the 51st shade of gray. Eat, pray, Charge!