Advanced intelligent animals can be trained to drag bodies and to haul items to storage. Dogs and Wild Boars are my pets of choice for that duty.
For a dedicated pet food area, it's a multi-step process.
1) use the "zone" tool to set up an Animal 1 zone. Assign a large area where you want them to be able to wander; make sure to NOT include your freezer area or crops.
2) create a storage area where you do want your animals to eat, within the Animal 1 zone
3) Change the settings in your freeze/colonist food storage and uncheck "Kibble" and "Hay"
4) Change the setting in your animal feeding area and uncheck everything except for Kibble and Hay.
5) go in to the "animals" tab and switch all your pets to Animal 1 zone. (if you have carnivores, you can leave them on Unrestricted if you'd like so that they can snag meat from your freezer)
Now your pawns will put human food in your main freezer and will put kibble and hay in your animal feeding area. Your animals, since they are forbidden from going in to your freezer, will eat the hay/kibble. One thing I like to do is keep the animal feeding area off limits during the warmer seasons and keep the Animal 1 zone so that it includes a lot of pasture land. The animals will graze on grass and bushes, which both grow back quickly. Once the snow starts falling, I open up the animal feeding area, which has been stocked with hay-grass and kibble.