What kind of phrase is warm weather?

"Warm weather" is a subject-predicate structure phrase, in which "weather" is a noun and acts as the subject of the phrase. "Warm" is an adjective and acts as the predicate of a phrase. The predicate component of a subject-predicate phrase can be a verb or an adjective.

There are a lot of similar phrases, such as pleasant climate, moderate temperature, gentle personality, outstanding temperament and so on.