Iwa, that's interesting!Q: Pourquoi avez vous quitté XXX?
R: À cause du temps.
Both of those you said are correct but not of the same register of speech, "N'aime pas le temps" pronounces like "N'ai pas le temps" and can be ambiguous when spoken.
Great, thanks for explaining!If the query was for a poll, "Je n'ai pas le temps (time)" can be a more frequent answer than "Je n'aime pas le temps (weather)" I wouldn't be sure someone heart the "m" sound, which I would merge with the nearby "p" sound, so I would add things or change the phrasing to lift the ambiguity. It may also depend on the regional accent, I think in south of France the "m" would be more pronounced.
In written register, as the question as in the passé composé, the answer would be "N'ai pas aimé le temps, le climat, la météo..."