I don't know if there's another name for it, but over here we call riding without a saddle and bridle, liberty style. I've slowly been teaching my mare how to do it. I started to once I realized that she already knows everything I want/need her to know, we don't show almost at all, and that she must be really bored. Lol
I started to do it with a rope halter w/ lead on in the arena.
I just hold the lead rope on one side of her to aid (if needed) with the turning and stopping.
She knows how to turn pretty well with my legs, and will stop when I squeeze with my knees while walking or trotting but she pretends like I'm not even on her anymore when I ask her to canter and goes where ever she feels like. Talk about being a brat. >.>
I was wondering if anyone rides like this, and if you do how far have you gotten and what did you have to do to get there?