I've seen videos of barrel horses running the pattern with no rider on their back. One that really knows his job knows exactly where to go. I've also seen one of a kid about five that his parents strapped him in the saddle with bungee cords and the horse ran the pattern. Not safe at all, but it was done.
My daughter will ride my wife's paint gelding around bareback with no bridle or hackamore, but she's not racing on him either. He already neck reined very well when we got him, so it wasn't much more of a step to ride him without bridle or hackamore. Most of the time, he's ridden with a hackamore though. I've rode my mare with a hackamore for a several months, but prefer a regular bit and she seems to as well (she got a bit argumentative with the hackamore). Heck, I won't even get on one bareback. I'm old enough that I don't bounce well if I hit the ground. As for a full gallop? I've been there, but prefer a nice smooth walk. I rarely get in a hurry about anything when I'm riding.
Eta: That clone is pretty interesting and I'm wondering how he'll work out on the barrels. I sold a palomino weanling last winter (out of my mare) that was a fast lil bugger. The young lady that has him now is planning on seeing how he does barrel racing in a few years.