Are there certain boots to protect your horse's hooves while sliding?

From your comments, your horse does not need shoes at all. Horses have better traction and ambulation in general when they are barefoot and it is better for the horse overall, regardless of discipline. My reining horse is barefoot, as are my other horses (cross country, jumping, dressage) and he is great without shoes. I do put protective leg wear on him on all four legs but it is just to protect his skin/pasterns/fetlock areas. The protective wear for his hind legs is made of leather and is for protecting his back legs for this very activity. You would not want to use hoof boots for reining. Since your horse is already barefoot, it is likely she has strong and healthy feet that are well calloused so she would be able to do any discipline just as she is. Just protect her legs. Her hooves should be fine. Usually hoof boots are used to protect weakened hooves that are recovering from the damage of shoes. Again, with healthy hooves, there would be no need for hoof boots. Good luck in your new endeavor.

I do not think you could get the competative slides you would need without without having sliding plates on your mare, it is the shoes that make it possible for a horse to slide 15 or 30 feet. and the surface of the arena.

Maybe E-Z boots would work?