I think "我喜欢雨天" is much more natral since "雨天" is an expression which means "rainy day".

It will be natural if you say"我喜欢雨天”， and it will be more natural and more popular if you say"我喜欢下雨天”， but we don't often use"我喜欢下雨的天气”

Yes,you can say "我喜欢下雨的天气",but "我喜欢下雨天" is more natural.

我喜欢下雨天