When my pony was put to sleep the vet warned that sometimes things do go wrong. Fortunately, Bandit simply laid down and appeared to go to sleep.
The important thing is that the vet administers first a dose to allow the horse to essentially "go to sleep" and then the killing dose. My friend had a horse put down in an emergency situation where the vet gave it all in one dose, and the horse went up and over backwards. It was very, very traumatic to witness.
My Arab gelding recently had to be put to sleep in an emergency situation where waiting for the vet would've caused the horse a great deal of pain. My older brother (an avid hunter) shot the horse with a rifle, and he died immediately. Because of his hunting backround, my brother knew where the right spot was to deliver the killing shot. I would not recommend this method to someone who didn't know exactly what they were doing.