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Herbivore/carnivore/omnivore refers specifically to what the species requires to live. Horses might eat the odd critter (I've watched a horse chase a hen and eat all her chicks), but they do not derive any sustenance from it and require nothing that plant matter cannot give. Supplements like salted fish are sometimes given, but serve no different purpose than giving a horse a salt-lick.
Dogs are a strange mix of omnivore and obligate carnivore. They require several substances only found in meat, but can digest starches readily as well.
Cats are less complex. They are an obligate carnivore in the purest sense. They gain very little from any starch source., and nothing from a plant is required for them to live a happy, purring (in some cases) life.