No, but you could do it.
I recently read about a couple who takes there 15ft mini cruiser across to the Islands from south Florida. If you head down to the Miami or the Keys and wait for good weather, then you should be fine. If you are in a hurry and decide not to wait for the weather you will pay dearly. The gulf stream crossing in winter can be really bad. I've known folks who had to wait three weeks for good weather. A recent article about small cruisers in the Carribean was in Cruising World Magazine.
