Horses are herbivores with specialized digestive systems.
Dogs (and humans) are omnivores.
Cats are considered by science to be obligate carnivores, with specialized digestive systems like horses. Cats can, however, benefit from pre-digested plant matter from the intestines of the prey they eat.
I'm not a scientist or a veterinarian, and I can only go by the information available to search at my fingertips. I encourage everyone with an interest to do the same.