Basically what everyone else has said is true. The first couple days of your trip will be more crowded then the end because people are still there from New Year's trips. As a PP mentioned, there's the Brazilian Tour Groups that ALWAYS go down in January, without fail.
The weather depends, Florida weather in January is kinda crazy. When we go down, you can always do hot tubs, just not always the pool. SM will be closed, but if you go to AK, you'll be able to do Kali River Rapids, as long as it's not like 40 degrees. The weather really is circumstantial, which is the main thing about going in January that's kind of unfortunate, you can't really plan everything out in advanced.
Hope you have a good trip!!