there is a reason armies stopped using horses even with decent armor then get hurt and killed easily by arty. Also regardless of how well trained the horse is its still a horse.
Now I want to make a runner that uses a revolver and drives a model T or a horse, he'd have to have a fabulous mustache.
I'd vote bayard or sabgarifya. What's cooler, a horse that turns to mist when you don't need it or scuba horse?
And they're smarter than most Shadowrunners, too!