This explanation is "straight from the Horse's Mouth".

Some say this is originally a boast of confidence from a racetrack tipster, who would say he gets his information from the horses themselves—thereby assuring the bettor that the info is the correct.

Another explanation is that a horse trader would persuade a prospective buyer with all kinds of talk about the animal, but for a clear measure of its worth, one can simply look in the animal's mouth. You can tell a great deal about a horse from its mouth. Age, nutrition, general health of the horse, and if it had been over reined.

If a horse is unruly you have to rein it in a lot, and this shows in the horse's mouth as well.

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