So, I live right near Tampa now (moved here from DC). It may or may not be cold. The weather really varies. But there's still tons to do.
Here's a few suggestions just off the top of my head:
A big thing that time of year is going to see manatees. They are magical. There are two places you can go see a whole ton of them in the area.
Crystal River:
https://www.facebook.com/VisitCitrus/?fref=ts
And Apollo Beach:
http://www.tampaelectric.com/company/mvc/
Clearwater is pretty boring (I think) but you can go do some stuff in the area. There's the Tampa zoo, which is nice. (And not abusive!)
Big Cat Rescue, like someone else suggested:
https://bigcatrescue.org/
Disney's just about an hour away, too, so you can certainly spend a couple of days doing that.
It's really nice around here, even in the winter.