Patrick, I think you are restricting your idea of what makes a good meal for a dog.
Sure, large livestock like steers and hogs are great food but there is a ton of meat available at other times of the year. Chicken, ducks, geese, quail and their eggs. Some people not only raise rabbits but also guinea pigs (thrive on weeds) or rats(thrive on table scraps). As more people are raising dairy goats the little males are pretty easy to find throughout the year. Some people also use fish and I don't see any reason why snakes and alligator wouldn't be fine as well.