I can go ahead and tell you that they're most likely not. Simply because I've yet to see an episode where they actually eat meat. All they ever have is like vegetable sandwiches and stuff like that. To answer your questions about why they keep meat animals, I reckon it's because they want the Milk from the Cows, the eggs from the Chickens, etc. Simple stuff like that
Vegetarians don't eat meat. Vegans won't consume anything that comes from animal production. Milk, eggs, and honey are included. Also, most sugar due to the manner in which it's processed.
Honey is actually debatable. But basically what he said, I tried veganism, but it is too hard and expensive. I am taking a break from vegetarianism and will go back on the 7th of January.
The animals are there just too destract the veiwers of the reason why ponies can grab items without hands. Or; Its all just contex to the story!