Sorry but seeing as this was a pitbull it had no business being let to chase horses. And no this is not breed bashing, I own a pit/rott. These dogs, if they ever actually catch a horse, will not stop. Luckily my dog got arthritis fast as when she was younger once she found out she could catch deer she routinely brought them home.
And since this dog doesn't seem all that well trained if it was running from the owner when she was trying to catch it, I would be worried what other training this dog lacks. A pitbull is not a breed to let training slack with.