I photographed this Mule Deer at Bryce Canyon National Park. What is this deer doing that mice and horses can, but pigs, cats, dogs, raccoons, and many other animals can't?
Deer, like most other herbivores, often chew their food from side to side. This grinds the food, instead of just crushing it. Grinding is much more effective for getting at the digestible parts of grass and other tough plants.
On the other hand, animals that eat meat (carnivores and omnivores) have teeth that make it difficult to chew from side to side, but that do make it easier for them to eat meat.