https://www.floridastateparks.org/parks-and-trails/paynes-prairie-preserve-sta
Check th Florida Parks web site. I frequent LaChua trail on the prairie and that does not have horseback riding or rentals.
The horses are wild horses. There are no rental type horses there.
There's the Hawthorne Trail that runs along the northeast border of the Park that is clearly intended for horseback riding. As far as camping with horses at the Park, i think you should call them. I doubt it is allowed.
There are horses there you should check with visitors center
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