The Master Horse is the gray horse whom Gulliver first meets when he's being attacked by Yahoos upon his arrival in Houyhnhnm Land. Gulliver thinks of himself as serving the Master Horse. The main reason the Master Horse appears in this novel is to hone Gulliver's comparisons of the Houyhnhnms and the Yahoos, but his way of talking about Houyhnhnms does cast some doubt on Gulliver's conclusions.
By the end of his stay with the Houyhnhnms, Gulliver has come to love them. All of his old hesitation about insulting England that he felt in Brobdingnag is totally gone now that he's chatting with the awesome Houyhnhnms. But the Master Horse does not seem a hundred percent perfect to us. He seems kind of stuck up, actually: he shares the astonishment of the Brobdingnagians at the idea that there could be other countries beyond the sea. And he practically calls Gulliver a liar (even though he doesn't know the exact word) when Gulliver breaks it to him that, in our neck of the woods, humans are the rational beings and horses are the beasts of burden. This self-satisfaction – one might even say smugness – in the greatness of the Houyhnhnms calls his virtue a teeny bit into question. How great can he really be if he's so arrogant?
Actually, this point about how great we're really supposed to think the Houyhnhnms are is one of the great debates surrounding Gulliver's Travels. As we've discussed in Gulliver's "Character Analysis," we know he's not an entirely reliable narrator, which makes his gonzo love of the Houyhnhnms a little suspicious.
Also, we're not the first people to notice that Gulliver's fanatical love of a herd of horses is a bit ironic. It seems especially so when he gets so homesick for the Houyhnhnms that he spends four hours a day back in England talking to his horses (which, he says, understand him "tolerably well" (4.11.18) – i.e., probably not at all). Critic A.E. Dyson points out that the Houyhnhnms seem too good to be true: after all, their society is one without love, energy, or really any reason to keep struggling or striving for anything. They just keep going on an even keel, not too happy, not too sad, but comfortable in their own excellence (source: A.E. Dyson, "Swift: The Metamorphosis of Irony," In Robert Greenberg, Editor. Gulliver's Travels: An Annotated Text With Critical Essays. New York: Norton, 1961, 316). Maybe the Houyhnhnms themselves are a satire of the pursuit of reason at all costs.
But let's not be too hasty in dismissing the Houyhnhnms: sure, maybe we don't have to agree with Gulliver's total faith in their greatness. On the other hand, the Yahoos do, legitimately, seem worse. We can see why, after his long voyages and exposure to so many awful people, Gulliver has decided to give up on humanity. This doesn't mean we have to as well, but we can still sympathize with his logic.