Caribbean in November has normally high enough temperatures to sunbathe, swim, snorkeling etc.
However, one can experience a cold front with strong winds and rain passing, but that is usually over after a day. Nights can get colder than usual. I remember returning to Miami one morning primo December when some water on the pier had frozen during the night. But that was something I saw only once. Other than that I've been on ships in the caribbean during three consecutive winter seasons and never experienced longer periods of bad or cold weather.