I was thinking about riding with my 9mm on my hip but then I have to deal with the police for killing a dog.
Secondly, in just about every state there are laws justifying the killing of aggressive dogs when they are threatening, attacking, or harassing people or livestock. I know my state's law on that chapter and verse and I will pull the trigger on an aggressive dog no questions asked.
Let the cops come. Who cares?
If my horse broke loose because of an aggressive dog I'd be beyond furious, and would be apt to shoot the dog right in front of his owner. Plus I have more ammo in case the owner gets uppity enough.