Your guess is as good as anyone's. In Florida we are enjoying a warmer than normal winter but with dire predictions that it will come to an end.
The eastern Carib is never below seventy. The trades see to that. Locals carry a sweater or jacket for the evenings because it seems cool due to the lack of humidity and for some reason the airconditioning in restaurants is always cranked up. Locals (lived there for several years) wear long sleeves in the evening but are outnumbered by tanked topped tourists.
In other words, pack for summer with a wrap of some sort just in case. Also a compact umbrella just in case although you shouldn't need it. In the summer we were comfortable while our guests died of heat stroke. In the winter we put something on while they enjoyed the mild temperature.
Incidentally, the Caribbean is a far better place to live than to visit.
Got my documents today so your's should be in hand. There is a lot more detail about the ship and what to wear when than is in the brochure. I got my answer about refrigerators in the rooms that no one saw fit to reply. It is going to be so Disney.
I am on the Jan 26 sailing also . It seems like there are very few disney posts here I finds tons of info at http://www.wdwinfo.com/ sorry I don't know how to do a link scroll down under cruise line click on cruise line discussion the message boards there get a dozen or 2 posts a day .
My 2 kids and I will be on the same 7 day cruise!!! The more south we get the warmer. It could be chilly in Miami but will warm as we progress.
Have cruised the Carribbean before, first time with my boys