Regarding the parameters affecting snowfall in the WEATHER txt:

My guess is that snow is affected either by the precipitation values with conjuction with the temperature values, that are given individually per terrain basis, or by the temperature values alone. This, however, is clear speculation and i have no clue how it would work. I'd try first decreasing the temperatures a bit more in temperate and some less in lush and play some campaign battles in such terrains.

Another, quicker playtesting way, is to do the same modification values that affect the custom battles, and try playing battles in different seasons. I haven't checked this, it is however possible that the two txt WEATHER files (custom and campaign) are different, as the former is related to mp and the latter to sp, the former has 4 seasons and the latter 2.

To those who dare: good hunting :)