Two winters ago we went down to Florida for 6 weeks (Feb. 1st-March 15) and camped at about 8 different campgrounds, some near the coasts, some in the central portion of the state. In the case of the central locations (Sebring, Winter Haven, Umatilla, Wesley Chapel) we never made a reservation and had no problem securing a site. We were looking to spend 3-4 nights per campground rather than a long-term stay. All three locations had multiple sites available while we camped there.
One suggestion if you're not planning to make reservations before leaving home: You might try phoning ahead to the next RV park a day or two prior to leaving your current location. That way you aren't going in blind. I would do this if you going to a more popular park or one located in a busy location like Orlando.
One thing that helped was that I did quite a bit of research on 35 different RV parks prior to leaving for our trip. I did this for various geographic areas of the state we planned to visit. I created a chart that included name & address, website & phone number, rates, amenities, comments & ratings from other campers (using RV Park Reviews.com), and actual directions like exit numbers and state routes. This was very helpful and allowed us to plan our next location easily.