The only problem i have with this idea, if this had a real impact on fights, most parties will probably end up standing around waiting for a certain weather condition.

An example of this:
This idea was used in FFXI aswell, Sandstorms and such boosted ground attacks

Side note:
while i feel like 90% of the player base never even paid attention to it, certain fights were much harder during certain gamedays AND weather. such as Titan, you would never enter the battle during earth day because his attack were much more effective, so if u were having any trouble with this fight you either simply waited till the next game day (about an hour rl time) or if u really needed help u had to wait for windsday (wednesdaylol!) which made his attack weaker.
Make of this as you will, does it really add to the experience? I feel like it doesn't add much, but some people really like that immersion that seems to keep coming up.

Side note II:
game day/weather also effected crafting, like crafting with fire crystals during a heat wave boosted chance of success. Again, thats cool and all, but should they really make u travel to the desert everytime u wanna make something out of a fire crystal? lol