They did a performance in Detroit....oh, I'm dating myself now...probably in the 60's since....when I was horse mad adolescent. I know they've been back several time since then. I still remember how amazing and incredibly graceful they were. If I recall several of the moves were combat-related, so the person could fight with free hands and the horse could defend their backside.... Or I dreamed up that explanation.
At any rate, they are beautiful animals!! Lucky you to get to go and see them.