Being a horseback rider and a roadie, I can say I prefer to speak at a reasonable volume when coming up behind a horse and rider. Don't shout, and don't just blow by. Either one would easily spook many a horse. There are plenty that wouldn't give a damn if you blew by at 50MPH with an entire marching band riding on unicycles behind you, but there are some that freak out if the car down the block has squeaky brakes.
I just make sure not to make any LOUD noises coming up behind a horse, but speak a sentence or two while passing. Cars have this habit of blowing their horn before passing a horse (sometimes to be idiots, but usually to let you know they're coming. That's not good at all. A horse can hear a freaking car coming!!) Just a "Hey there, coming up behind you, nice ride, man" is plenty. Lets the horse know there's a human back there, lets it know it's coming up fast and lets it know it's said human while you're passing. It also allows the rider time to get ready for whatever may happen. JMO

Cole