The horse camp appears to be closed right now. Been to the park many times this past 2 months. Haven't seen any activity.
Download the app Florida outdoors you can make reservations online and check availability
Yes, state parks have an 800 reservation#. The problem that i found is that, of course, they have no knowledge of the parks' layouts, so they can't really make recommendations. I did call j Dickerson, directly, though. I just Google them and got their phone#. Not at home, so don't have brochure, to give it to you. Sorry. Keep calling, you'll get through. Ask them questions, then make res thru 800# that they give you.
If you go to the website for Jonathan Dickinson State Park you'll be able to make a reservation the park doesn't make reservations at the number that you called goes to the ranger station you have to do through the 1-800 number on the website
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