Even if ponies are technically omnivores, they are stated to be vegetarians (Over a Barrel,Pinkie’s song). So eating meat would be socially unacceptable. Any ‘meat’ would be a substitute to simulate old and/or foreign cuisine.
Ponies are omnivorous, so I don’t see the issue with them eating meat as long as its not from another sapient creature, so basically pigs and chickens could easily be on the menu.