The park does provide a good-sized gravel lot to park your own horse trailer, with hitching rails and running water. There aren't any turnout paddocks though (the Biltmore House for example has turnout paddocks which means you can do overnights there.) With the modern slant-loading trailers with feed storage, tack rooms &c. you really can bring everything with you that you need for a day's ride.
Golf carts wouldn't do it - too steep, especially around the last action of the battle (Snodgrass Hill area). I can just see having to struggle to lift cart and occupants out of the ditch every 20 yards or so . . . ;-0