Though walking is the slowest of all their paces, his step should be light, brisk, and neither too long nor too short; his carriage should be easy, which depends much on the freedom of his shoulders, and is known by the manner in which he carries his head in walking; if he keeps it high and steady, he is generally vigorous and quick. When the motion of the shoulders is not free, the leg does not rise enough, and the horse is apt to stumble, and strike his foot against the inequalities on the ground. A horse should raise his shoulders, and lower his haunches, in walking; he should also raise and support his leg; but if he keeps it up too long, or lets it fall too slowly, he loses all the advantage of his suppleness, becomes heavy, and fit for nothing but to match with another for shew and parade.

It is not sufficient that his walk should be easy, his steps must be also equal and uniform, both behind and before, for if his crupper has a swinging motion while he keeps up his shoulders, the rider is much jolted, and rendered uneasy; the same thing happens when the horse extends his hind leg so much as to rest it beyond the same place in which he rested his fore foot. Horses with short bodies are subject to this fault; those which cross their legs or strike them against each other, are not sure footed; in general those whose bodies are long, are the most easy for the rider, because he is at a greater distance from the two centres of motion, the shoulders and haunches, and therefore less sensible of the jolting.

Buffon's Natural History. Volume V (of 10) — Part 48

The usual method of walking among quadrupeds is to lift, at the same time, one of the fore legs of one side, and one of the hind legs of the other. As their bodies are sustained upon four points of support, which form an oblong square, the easiest manner of moving for them is to change two at once in the diagonal, in such a manner that the centre of gravity of the body of the animal may rest always in the direction of the two points which are not in motion. In the three natural paces of the horse, the walk, the trot, and the gallop, this rule of motion is always observed, though with some difference. In the walk there are four beats, in the movement; if the right fore leg moves first the left hind leg follows the instant after; then the left fore leg moves forward in turn, and is followed instantly by the right hind leg; thus the right fore foot rests on the ground first, the left hind foot next, then the left fore foot rests, and lastly, the right hind foot, which makes a movement of four beats, and at three intervals, of which the first and last are shorter than the middle one. In the trot there are but two beats; if the right fore leg goes off the ground the left hind leg moves at the same time, and then the left fore leg moves at the same time with the right hind one, in such a manner, that there are in this movement only two beats and one interval; the right fore foot, and the left hind foot, rest on the ground at the same time, as is also the case with the left fore foot and the right hind one. In the gallop there is usually three beats; but as in this movement there is a kind of leaping of the two fore legs, the right ought to advance more forward than the left, which ought to remain on the ground to serve as a point of rest for the sudden jerk he takes: the left hind foot moves the first, and rests the first on the ground; then the right hind leg is lifted up conjointly with the left fore leg, and both rest on the ground together; and lastly, the right fore leg is raised instantly after the left fore leg and right hind one, and rests last on the ground: thus in the gallop there are three beats and two intervals; in the first interval, when the movement is made with haste, the four legs are, for an instant, in the air at the same time, and the four shoes may be seen at once. When the horse has supple limbs and haunches, and moves with agility, the gallop is the more perfect, and the cadence is made in four times; first, the left hind foot, then the right hind foot, next the left fore foot, and, lastly, the right fore foot.

Buffon's Natural History. Volume V (of 10) — Part 48