It is not your fault, it is the dog owner's fault for allowing their dog around horses. I try to let people know about the danger of dogs and horses. My horse had several "accidents" with dogs, ran over one, kicked two more with no major injuries except one dog had a broken tooth. Then she kicked my dog in the head and I realized these were not accidents, she was trying to harm the dogs.
Many people have their dogs around horses and have not had problems. I had dogs around horses for many years. I believe people are still risking their dog's life, and need to be told that. The nicest horse might have a bad day and kick the dog, and then the dog will be seriously injured or dead. After my dog got kicked, the vet told me they take care of many, many dogs and cats each year that are injured or killed by horses. My dog survived and is fine, but it was a very large vet bill. I am just glad my ignorance didn't cost him his life.
It's never the horse owner's fault if a horse injures or kills a dog. It is to be expected when a 1,000 lb animal is loose with an animal only a fraction of it's size. People are very ignorant of this, and when dogs run up to our horses on the beach I say loudly, "Careful, don't kick the dog," and then people suddenly realize their dogs may be in danger and come gather them up. For some reason they think the dog is the threat to us. Dogs do bite horses sometimes, and injure them badly, but I know my horses would kill any dog that bit them.