This link shows a number of places to stay. We found central Florida fairly easy to find places. We stayed in a state park for a month. (There is a 14 day maximum stay in Florida but you can go somewhere else for a night and then come back.) I had to cobble together different sites in the park for different days but for late December reservation for mid-January to mid-February I think I did quite well. You can use Reserve America to see what's available.
Florida Snowbird RV Parks â€“ St. Augustine, Naples, RV destinations from Good Sam Club
We also spent 2 nights at a Carefree resort in Zephyrhills. They have quite a few around that area and it's only 45 miles from Tampa; also not too far to Disney and Orlando, maybe 50 miles (he said, guessing). There's a nice Camping World close to there too. Carefree resorts are also online so you can see what's available, but call instead of using the online. I think I was only the second person to make an online reservation at Settler's Rest. They have 3 in a row there, try to get something away from the road.
Florida RV Parks | Find RV Parks in Florida | Book resort reservation
When we were shopping at Walmart, an owner(?) of Travelers Rest Resort & Golf Course in Dade City approached us as we sat in our AS having lunch. She told us about their place which used to be an all AS park but now they were letting in SOB RVs. We went over there to check it out and it is quite nice. It was worth the trip just to see all of the old trailers and the huge AS RVs. There were all sorts of set ups and they had room at that time. If you're into golf, their course was beautiful. They had lots of planned activities and the resort was quite large. Everyone waved at us as we drove through and they seemed quite friendly.
Travelers Rest RV Resort and Golf Course, Dade City Florida
Anything in large cities is hard to reserve or further south of Tampa is also difficult. The further south you go the harder it is to find anything. Central Florida is very nice, very affordable and available. This was our first year as snowbirds and we stayed only a month. Came back to 15" of snow and -18*F weather. Next year, 2 months or maybe 3. Current plan is to leave after Halloween and return in mid-March or later.