While the story initially leads the reader to suspect the stable-boy, John Straker, the true culprit is revealed to be the horse's owner, Colonel Ross. He had a motive – a gambling debt he owed to the murdered trainer, and he planned the crime meticulously to frame the horse for the trainer's death.
Here's how he did it:
* The "silenced" dog: Colonel Ross, aware of the dog's protective nature, used a piece of the trainer's own tobacco to keep the dog quiet.
* The "missing" horse: He had his stable-boy lead Silver Blaze away from the stables, making it seem like the horse had run off with the trainer's body.
* The "clueless" horse: Colonel Ross, a skilled horseman, knew how to train a horse to stay quiet, thus ensuring Silver Blaze remained calm and "clueless" about the murder.
It's a classic example of Conan Doyle's masterful misdirection and detective work by Sherlock Holmes!