Welcome aboard, Luigina! My family has set sail with Disney Cruise Line in February a few different times and have always found the weather to be very nice. Typically, the Caribbean has highs in the low 80's and lows in the low 70's during this part of the year, so summer wear is certainly appropriate.
I suggest that you go online and check the weather forecast for your ports of call about a week before you set sail, just to be sure about what to pack. No matter how warm it will be, I always suggest packing a sweater or light jacket for those cooler days and nights and the breezy evenings on deck. Additionally, I can get a little cool inside the ship in the restaurants and theatre at times, so I like to have an additional layer with me.
Towels are always available on the pool deck, so no need to pack your own. If you book one of Disney Cruise Line's
Port Adventures that involves water, towels will be available for you to bring off the ship when you meet up with your group for the adventure. This certainly saves valuable space in your luggage!
Have fun planning and enjoy a very magical cruise on the Fantasy, Luigina!