I agree with everybody elses sentiments on this subject. On a personal note, my horse DOES stomp dogs. She has killed two in her 24 years and once was while under saddle. She actually charged after another one that got in her pasture once, stomping it to death, and it was a pitbull. She will leave dogs alone if they let her alone though, but chasing, jumping at her and biting her will get them killed everytime. When I first got her I used to ride with a short bat to use on attacking dogs, but it soon became apparent to me that unless there was more than one at a time, my horse could handle the situation herself. She never bothered my own rottie and they would play tag together out in the pasture. It was so cute to watch. He'd chase her across the pasture, running alongside mostly not behind, and they'd stop in the corner to rest and catch their breath. Then, she'd take off chasing him back the same way again. They would repeat the process many times over throughout their lives. I think they became good and respectful friends.
