As John Lyons says, you have 3 seconds to KILL a horse that bites you,
short of having a gun, one can't actually kill a horse in three
seconds but the horse needs to believe that you
could!
If there were many horses in even moderately close quarters,
going after one's horse like this causes the horse to back up,
spin, do anything to get away--oblivious of any other horse
or person in its path. The reaction spreads like dominos.
It could easily be more dangerous to more people to
correct the horse in this situation than to let the misbehavior