What zombies eat, remember Herschel was tossing live chickens into his private zombie zoo and zombies attacked Darryl's freshly killed deer in Season 1 so pretty much any fresh meat will do for a zombie. However, it does not appear that they starve to death (tough to do when you are already dead) quickly since they are always running into zombies that have been confined (a year of TWD time has passed I think). Obviously, if your metabolism does not have to deal with those pesky body functions like keeping you warm, breathing and oxygen exchange, a whole host of enzyme and chemical reactions or any kind of exercise then a little nourishment must go a lo-o-o-o-ong way.