I grew up in Central Florida, about 45 minutes Northeast of Orlando, and most days that time of the year are pleasantly mild. We're talking somewhere in the range of 60-80 degrees for the highs and 45-65 for the lows. There are definitely cold snaps, though, and they tend to hit hardest in January.
Two years ago, we were in Disney early to mid January, during the marathon weekend, and it actually sleeted the night of the marathon. For a good four days, the highs never got over 50. It was gray, windy and sometimes rainy. It happens. The thing is, two days after that sleet storm, the high hit 70, and it was a beautiful, sunny day.
Best advice for a Florida vacation for that time of the year: It's mostly jeans and t-shirts, but watch the forecast all the way up to the day before you leave just so you can plan for those possible, but short-lived, drops in temperature. Otherwise, light, easy to carry layers are your friend for those chilly mornings and evenings.