I had the two horses I currently take care of in the arena today. I rode the smaller one bareback, and the other one run free. It was such a nice experience. The horses, both geldings, know each other from the pasture, they are in one herd, and the one I was on is the alpha (which is decent when riding as the other horse can be easily directed). 
I had no idea what would happen and was just experimenting. When I turn them loose, they often go separate ways in the arena, with the big Frisian exploring and wandering around and the warmblood relaxing and not moving a foot.

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