1. 天气 means "weather". It may changes harshly in a day.
气候means "climate". It's a long-term, general weather conditions in a place. For example, we say "climate change" as "气候变迁"
basically the sentence can be understood but I suggest you add some words to make it more nature.
For example, add "那时候"(At that time)before 风刮得很大.
I think It would be more nature; )