I've done it several times. The weather is terrific, especially the S. Caribbean. Just a few degrees (5 or so) off of the summer heat. This is the last month of hurricane season though, although Nov is a fairly inactive month for hurricanes. I'd recommend flying in a day early. The real advantages are that the rates are rock bottom and there aren't as many children on the ships
this past november, i went to barbados, st. martin and martineque...i live in florida, but it wuz a very nice temperature on the islands most of the time...although in martineque it did rain during our tour of the island.
My husband and I had great weather in St. Thomas/St. John over Thanksgiving a few years ago. Nothing but beautiful blue skies and tolerable temperatures. The water for snorkeling was also very warm. I couldn't tell the difference between the air temperature and the water temperature.