I used to do this a lot. I never trained them without a bridle. I never rode in a halter. I just hung the reins on the saddle horn until I was ready to get everything done without having to pick up the reins and could get it done VERY WELL.
But, leading up to that point, when the horse leaned a little here or pushed a little there, I would instantly pick up the reins and correct the horse -- pretty harshly if I thought the horse was taking advantage of the situation.
I rode with a neck string for quite a while (while keeping the bridle in place) before riding without the bridle there for a back-up.
I made sure I had good flying lead changes, very good speed control and very good stops before I ever did free style classes or demonstrations. Then, for all of my practice sessions, I would still have a bridle in place. I never used a halter -- only a neck string.
I have watched Stacy Westfall quite a bit and she also keeps a bridle on when she practices so she can correct very quickly and with firmness so the horse does not learn to take advantage. Of course, she takes it even farther by riding without a neck string for classes and demos. I find this much more difficult, mainly in her ability to keep a horse's nose to the inside throughout circles and lead changes.
I have seen many reining horses that performed their best stops in the free style classes where their riders could not pull on them. This speaks volumes.