That's called a wild horse race in rodeo. It's done all the time and usually, the cowboys are hurt alot worse than the horse.
Any behavior that ignores the realities of deliberately allowing a horse to run loose with a lead rope hanging to the ground would benefit from being brought into the 21st century. The fact a film studio's animal handers might have once had their teeth knocked out by a horse or a couple of bulls tells me just how backwater and unprofessional the operation apparently is.