Its a good idea, but i would change some things. Ill just throw some random ideas:
Have the weather as a world tile state: a tundra plain tile can suffer from rain,sun,snow, high wind... same for everything. Different weathers cause different effects, maybe sun being neutral, rain boosting slightly food production in the tile, but lowering a bit melee damage done in that tile... same for every effect. Of course, snow in the tropics would be really strange, and so on.
I wouldnt limit this to just army boosts, but implement it as a new game mechanic, affecting more aspects of the game, like speed of units in travel, resouce production, army damage... or even some special effects for rare weathers. Example, raining in the desert would boost food a lot, slowing down movement a lot.
Theese effects would change depending on your zone: sun in the desert would be the "default" state, and rain would provide X bonuses and disadvantages. Rain in the tropics would be "default" state, with sun providing Y bonuses and dissadvantages.
Deserts and glaciers would be the most stable zones, with almost always the dafault weather, but with large bonuses to the others, while intermediate zones would have more changes in the weather, but lesser buffs. Rare weathers would be the exception.
This mechanic would work in zones. The "default" zone would be like a background: if the tile is not under the effect of the Z zone, the zone is "default".The first way i can think of is that different weathers work like culture in domains: a Rain zone in the plains, where it's NOT default, will have X number, that depends on the size you want it to have. Make it so it turns into a 2nd grade equation of (y^2+yx) form, with y beeing the time the weather zone has been active, so the number grows first and then shrinks. Then have a determined number table like "if the numbers > than 3, it will have 1 cell of influence, if the numbers > than 9, 4 cells in a circle like pattern..." and so on. The places where the first cell of one weather appears would be random, with stranger weathers appearing less times.
I know this is too big to implement as it is,but you said posting ideas is fine, no?