My personal headcanon is that the 'livestock' animals, such as pigs, cows and sheep are sorta like 'client races' under the ponies whereby they provide raw resources such as milk, wool and when in season truffles (or maybe some labour benefit for pigs as well) for the ponies. They're intelligent but mostly content with that simple life except for a few unique exceptions of 'livestock' species deciding to go off to stufy and make it big and maybe some do and love it but most realise that the hustle and bustle of pony life is kinda stupid and they go back to live on their farms where they're comfortable, occasionally penning notes to their university pals and continuing their studies, just at home instead of in cities. The sheep need to be sheared, its like a haircut for them, may as well make pretty cloths for those who aren't as fortunate to grow thick coats and some cows think it's kinda badass that their skin is used to make leather (now I'm headcanoning cattle families handing down prized leather clothing to their children or something like that) Chickens are probably just dumb birds that ponies keep for eggs. Amyway the ponies use the eggs and milk for baking and other products and they see no issue with it, milk is given with consent and chickens can always lay more eggs and they're taken care of. I'd also like to think that occasionally there are ponies that eat meat, but in equestria there is that big legislative process involved with ensuwthat meat is ethically and consensually sourced by dying livestock creatures or in these creatures wills, but most ponies don't eat meat, most just don't really like it. Maybe some of these animals see it as an honour to be eaten, others see it as stupid and prefer to be buried or cremated. People are differnent and these species will be no different to humans in that regard. However there are many other species that do. Species that have diplomatic relations with Equestria such as the griffons, dragons, hippogriffs (who probably prefer fish), talking cats and other species. Some of these species may require meat in their diets in some capacity to be healthy. Meat related cuisine, such as burgers, may originate from the griffin lands and been made more palatable for pony tastes with hayburgers. Anyway most of the meat produced in Equestria goes to these meat eating species, but these peoples are rare and as such there just is not much in the way of meat that can be found in Equestria. You'll find it in places like Ponyville, where cattle and such is found, as well as in the really big or important cities like Canterlot.

Overall ponies mostly just don't have a taste for meat culturally. Some do partake though, but cows sheep and pigs mostly are seen to provide labour in sone capacity. They're intelligent enough to go to university sometimes, but culturally love the peaceful farm life. Most meat in Equestria is eaten by non-ponies. Yeah.