CQ, the temps in Florida can vary quite a bit in January, but you won't have to face ice or snow.
After living here for two years I would have a hard time facing the long winters in Ct.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Independence of the Seas 12/29/2013 Top-notch!