I've driven horses. First, if the horse is panicking, a steady pull on the reins isn't going to phase them. Saw the reins, jerk the reins, get the horse's attention. Keep your voice soft and calm.
I think the drivers should have gone to the middle of the ring, gotten out of the carts and held their horses' heads. Let the other people keep the runaway away from the other rigs.
And it just has to be said: How much more pretentious can the judges get, than running around with lab coats on??! Rediculously silly.
Of course this is all hindsight. Except for the dooffus judges and their lab coats.