Well, breeding animals should be enough to feed your family if you have a cooking hearth. Breeding Sheep gives you 2f per harvest, Boar give you 3f, and Cows give you 4f. That's 9f per harvest once you have them all going. The problem is having space for all of the animal types, then getting your hands on them.
One card that helps with both those aspects in 4-player is Animal Breeder. He allows you to buy animal pairs whenever you fence unused spaces. He is one of the best cards in the game, and I almost always pick him first in draft. If you fence early and fence often, you can get all animal types breeding very quickly.
There are generally more animal-based Occupations for 4+ players. For example, Cowherd and Swineherd (similar to 3+ player Sheep Farmer and Animal Dealer) let you take an additional animal when you use the appropriate action space. If you are using expansions there are even more. Dove Hunter from France Deck lets you turn 1 sheep into 4 food (or 1 cow into 6 food) every harvest.
These are just a few of my favorites for animal-based feeding. There are plenty of others, though.