January is the perfect time to see the Everglades. Few bugs and warm (not oppressively hot and humid) temps.
Key West is a fun place and there are several historical things to see: the lighthouse, the Truman's Little Whitehouse, The Flagler Museum. All these can be seen in one day or even long afternoon. Key West is tiny.
The further south you go/stay the warmer the temps. Of course "cold weather" to someone who lives year round in Florida has a very different meaning to the rest of the world.....LOL