This one comes along without any attribution or story, but it's not hard to believe.
I myself saw a horse and a dog fight in my youth.
It started out with the dog wanting a bit of fun - playing like he would with any other dog, repeatedly nipping at the horse's heels. Giving him the business.
The horse, who was generally very good-natured, didn't enjoy the game; and after a few minutes of it, was getting tired. Eventually he kind of fell over on his side. The dog took the opportunity to take one more nip at the horse's heels -- except that the heels were now free to kick out, which the horse did, catching the dog's midsection.
The dog wasn't seriously injured, but it did run across the yard making the traditional "yipe-yipe-yipe" sound that a hurt dog will make.