According to a misguided article on Boingboing.Net, the Living Dead wouldn't stand a chance against Animals. Now, I'm not at all a fan of Zombie Shows, or of the very idea of zombies. To be honest, they give me the creeps. But when I read this, I had to say, "Now, wait just a minute. This isn't right--it's clearly a case of someone riding on their hobbyhorse." In the article, National Wildlife Federation naturalist David Mizejewski explains how he thinks nature would deal with a zombie outbreak: brutally, and without quarter. Where he goes off the rails is his wanting to specify that zombies are merely walking carrion. Sorry, but I am not buying it. It is like saying that the Late Roman Empire could have easily defeated the invading Barbarian Hordes, if only all of the Barbarians had casts on their legs.
First is the problem of whatever causes Zombification. If it's a pathogen that can instantly infect an attack victim, why couldn't it infect an animal that bites or eats a part of a Zombie? Any condition that could accidently produce an organism that can simultaneously hijack the Human Body and Brain, could just as easily produce ones that would affect animals.
If the causative agent was artificially produced in a laboratory, early versions of it would no doubt be tailored for and tested on animals. If you were evil enough to do something like this, you'd quickly realize that it would be easier and more economical (and frightening) to just infect animals and let them do all of the attacking. Even simpler, then, would be to produce a sort of super-Rabies that was fast-acting but didn't quickly kill the host.
Second, even if the cause of Zombification was strictly human-specific, and could neither infect any other creature (down to the microscopic) nor mutate, there are still two major objections.
Problem A is the motility issue. Birds in general are serious motion detectors, and Carrion Birds don't go after things that are still moving. Crows and ravens might, along with coyotes and bears, etc., but that would only be in the case of a very slow moving and isolated Zombie. Ones moving around in groups would be safe from carrion eaters. It is not known whether Zombies sleep or have rest periods, so it can't be posited that there would be times that they weren't moving, and would be just lying or sitting on the ground motionless where they could be easily accessed by bacteria, fungi, molds, and spores, or carrion-seeking insects.
Problem B is the question of what Zombie flesh would even smell or taste like. Given infection by some pathogen that caused the flesh to be alive and dead at the same time, Zombies might not be attractive to carrion seekers, or might even actively repel them. They might also be poisonous and kill anything besides another Human that bit them.