Try searching for RV parks instead of mobile home parks. Mobile home parks generally mean permanent residents. But be prepared to be disappointed. In the winter, everyone east of the Mississippi river with an RV is already headed for sunshine. And they made reservations last summer.
I can recommend Sun N' Fun, in Sarasota near the west coast, but it isn't beachfront, and it isn't cheap, but they have 800 sites. Nothing on either coast of Florida is cheap in the winter. They have FHU pull through sites plus cable TV, and all kinds of activities. I was visiting friends that lived near there, so I didn't take advantage of all the amenities.
Here's the link.
Retired and visiting as much of this beautiful country as I can.