You should change the full stop (after "I don't just dislike the weather") to a comma. But otherwise, yes, it's grammatically correct. It's probably worth noting that some people feel that we should only use the word "hate" or the word "love" for intense emotions... but people do use these words in everyday speech for things that are unlikely to provoke really strong feelings... and anyway it's really your decision how you feel about something, so if you think that hate is appropriate for the strength of your emotional response to the weather, well that's your choice