I own two Arabs, and it takes an incredible amount of training to get a horse to hop or jump on command. It is easy for a horse when it sees a jump to jump over it, but extremely hard to get it to hop on command. Many horse breeds are simply incapable of learning it also.
It takes many years of training to get a horse to do this and I doubt they had the training techniques (modern day behaviorism) then that we have now that allow the horse to learn the command "easily."
The famous Lipizzaner Stallions are among the horses in the world that can do this, and I really doubt the horses of even elite cavalry units were trained anywhere near that well. So as for the hopping on command, it simply isn't historical.
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