I know that my horses know walk, trot, canter, whoa, back up, scoot over, quit it, stand, and a whole slew of other voice commands.
However, I don't know if they would respond to someone over a loud speaker. I have never tried.
I know that these voice cues are essential to teaching lessons - if a child is asking a horse to do something with his or her body, and they are just learning, the horse sometimes doesn't understand, and I can ask the horse to stop or back or walk from a distance on the ground.
They are great for lunging, or when navigating through a crowded barn (i.e. "scoot over" to a tied horse when I am leading another horse.) But perhaps my horses read my body language and my tone as well as hear the words. I am honestly not sure.
I have noticed that horses at horse shows do respond to announcements before their riders ask, very often.
I think it depends on the horse and the person, and the language they understand each other in best.