Well then, I guess you won't believe that Okie likes to chase dogs then:')
So does my pony.... she'll go after a dog, but that is really defensive and territorial... like the cow or deer who will run a predator off a calf. They chase them because deep in their instinct they percieve it as a threat, even though in their experience it is more like a game.
Rather than being 'reactive' like running off a dog or a lower horse in the pecking order, a cutting horse's behavior is distinctly proactive and stalking, very cat-like in the way they look at the cow.