This answer centered mainly on the “hep” in “hep hep hurrah,” inconclusively musing that the expressions could come from herders’ calls. Which seems very plausible to me. However, I did read recently that “hurrah” or “hurray” comes from the Mongolians of Genghis Khan’s time. It would make sense that these nomadic herdsmen, who probably contributed a great deal to equestrian and herding practices the world over (considering they eventually oversaw an empire that stretched from Eastern Europe to Korea). Has anyone else heard of this connection?
Highly unlikely.
According to the late George MacDonald Fraser “Hip hip hooray” was an ancient Briton war cry.