Not really weather, but have the the nights/days be longer/shorter depending on the season. It's just weird having 7PM in game be late evening while the sky outside is pretty blue.
I feel like this might be because it doesn't change that much in Japan. Like right now it actually does get dark at about 7 here... In the winter it gets dark a bit earlier at like 5, but overall, it doesn't change as much as it does in Europe (at least that's how I feel now I"ve moved here xD)