[Hrum]

Someone around here can probably answer your question better than I can, but I believe in addition to the strategic map effects you mention, there's an encumbrance effect on the battlefield.

I believe units that have the appropriate (frost/fire) resistance are unaffected, but for anyone else fighting in a climate raises their encumbrance. For example LA Mictlan guys (prefer Heat +1) fighting in a province with Hot3 suffer more encumbrance per round of melee and casting than they would otherwise. I think the encumbrance change is the only battlefield effect of non-ideal climate for units, unless they have cold/hot power (more stuff affected) or resistance (nothing affected).