Horses chew by moving their lower jaw in an oval pattern because their lower jaw is narrower than the upper jaw. As the jaw closes, it moves from one side to the other. As it opens it returns to the original position.
sideways
Horses chew their hay or grains in their mouth with their teeth so that it is easier for their stomach to digest. Horses chew from side to side as in a motion of a grinder.
they chew on food
To chew their food.
Horses chew wood but they gain no nutritional benefit from wood.
they eat with there mouths and chew with there teeth
Same as domestic horses; teeth developed to chomp down on and chew grass.
Cows, and any animals that chew cud (ruminants), have a four chambered stomach. Horses do not chew cud and only have a one-chambered stomach. (pseudo-ruminant monogastrics.)
Horses can't actually cut through would, but they do chew on it (usually called cribbing).
Cows, sheep and goats chew sideways (or rather in more of a circular motion) too. It's an adaptation to break down plant matter that they're chewing faster and more efficiently than if the jaw movements were straight up and down like with us humans, a wolf or a tiger.
Grass is really hard to digest so they have to chew down the cell wall of the plant to digest it otherwise it'll come out exactly the way it was when it was eaten.
Believe it or not there was at least an informal study done on this exact thing. In stock trailers (trailers with no dividers) horses seemed to want to stand slightly sideways or diagonally. They would do it over and over. The conclusion was that they could balance better in this position.