Very interesting question, Ron! Depending on what you mean exactly, we might need a veterinarian's opinion. Would a horse fed only meat be able to survive? I'm guessing it could, but that it wouldn't be very happy--since it's "designed" to eat grass. Still, it could probably extract enough calories from the meat to keep from starving. The flipside: suppose a dog was fed only grass? My hunch is that this poor dog would not survive--grass having very few calories--that is, it contains very little energy. No matter how much grass the dog ate, it simply couldn't sustain itself. (The reason horses can get by eating grass is that they are large, which allows them to survive by eating large quantities of low quality food.

Compare what large mammals eat versus small mammals. Elephants generally eat low energy food such as bark, twigs, and leaves--although they're happy to eat the occasional peanut or other tasty morsel when they can find them. On the other hand, mice favor things like nuts and seeds--foods rich in calories. For reasons having to do with geometry, large mammals burn fewer calories per pound/kilogram of animal, than do small mammals. This explains why two five-pound dogs would eat more collectively than does one 10-pound dog, for example. It also explains why there aren't any whales the size of goldfish--but that's a different story.)

Over much longer timescales, we may ask whether it's possible for a carnivorous group of mammals to produce a plant eating side branch, or for a herbivorous group to have carnivorous descendants. Here the answer is at least partially yes. Carnivores (lions, dogs, seals, etc.--members of a group of mammals called the Carnivora) almost certainly had ancestors with more generalized diets. Paradoxically, although the ancestors of Carnivora were meat-eating, some members of the group have secondarily become herbivorous--pandas being perhaps the most famous examples.

Has a group of highly specialized herbivores, say cows, ever given rise to meat eaters? Possibly, although among mammals, I can't think of any good examples of this. The important point is that over millions of years, evolution has managed to transform mammals that ate one kind of food, into mammals that ate/eat completely different kinds of food.

Stay curious and keep asking questions!

That’s a great question. One of the things I tell my students is that people like to make nice, neat categories for the natural world, then the natural world never fits neatly into them.

One good example is when animals that we think of as vegetarians, or herbivores, eat bones. Mammals need calcium and other minerals to build bones, teeth, and other things. When a mammal is pregnant or giving milk, she needs a lot of calcium. Plants generally don’t have a lot of calcium. So mother mammals chew on bones, even if they mostly live on plants. They don’t usually hunt small animals, but if they get a chance to eat a baby bird or a mouse, they probably will. Male mammals making antlers also need a lot of calcium.

Herbivorous mammals don’t have the tools to be good hunters. Their feet, teeth, and even the placement of their eyes are good for eating plants, not hunting animals. They probably wouldn’t stay healthy on an all-meat diet, but adding some meat gives them more protein, calcium, and other nutrients. That’s why companies that make food for cows often put animal protein in cattle feed.

Some carnivores, like cats, cannot become pure herbivores. They need some proteins from their food that they can’t make on their own. That’s why cats can’t live on dog food. It won’t poison them, but they won’t get all the nutrients they need.

How are the feet, teeth, and eyes of a deer different from those of a cat? Why do you think those differences are important?

What animal eats is a spectrum. On one end, there are herbivores that mainly subsist on plants. On the other end, there are carnivores that mainly subsist on other animals.

Omnivores falls between those two ends of the spectrum

There are animals that are obligate carnivores. They cannot survive without meat. For example, cat is an obligate carnivore. This is why forcing cats to go vegan is cruel.

With very few exceptions such as koalas, there are no other strictly herbivores. Although those animals do not hunt, they will eat meat when the opportunity presents itself. Those opportunistic carnivores include pandas, deers, cows, goats, chickens, ducks.

This is complicated, but the short answer is "yes".

First, most plant-eating mammals do eat meat if it is available; they just don't have the ability to hunt and kill it for their own. Deer, for example, have been photographed eating dead rabbits that they come across, even though deer normally eat plants.

Second, evolution happens. It is thought that the land-going ancestors of whales ate plants in the very distant past, but they evolved to become meat-eaters.

For people, it's fine, and for apes and other primates in general, because we're omnivores - we eat plants and animals.*

Other animals seem to have lost genes and things needed to eat meat if they became herbivores [vegetarians]. They lost genes and things needed to eat plants if they became carnivores [meat eaters].**

*Most primates became omnivores early in their existence, and stayed put. "We seem to hang out in this omnivorous role." It's easy to imagine that there's an evolutionary advantage to being able to eat just about anything.

**Convergent gene losses illuminate metabolic and physiological changes in herbivores and carnivores. 3036–3041 | PNAS | February 19, 2019 | vol. 116 | no. 8

The following is a great site to learn about what happens when feeding meat to a herbivorous animal.