Far as I am aware of, no. To my understanding weather is basicly randomized which would make any attempt for us to know when it will useless. There are however areas that experiance a 'season' In Zi'tah for example during the summer of a Vana year it goes into a monsoon season and the rain weather picks up greatly.
Don't really, it's just something people found out about Zi'tah as Noble Mold only spawns during that time period. Don't know if there are others, Zi'tah may be the only one with a season.
Rolanberry and Batallia can get ice weather during winter months. Valkurm is more likely to get fire weather (usually around 13:00) during summer months.