Apparently the practice is alive and well, too. Was driving down the road the other day and saw 8 coyote carcasses hanging from a fence row. Smelled awful, but I guess the buzzards were happy.
Edibles (read good to eat) go into the freezer.
Predators/furbearers get skinned and turned into something to stay warm in.
Pests lay where they fall and go on to feed the ravens and eagles.
Regarding game animals, I just don't shoot what I am not willing to clean and eat. So far as varmints are concerned, thats another story. I don't mind killing them at all. The rest of the furred or feathered animals have nothing to fear from me.
It all depends on the location.
Prairie dogs... I leave 'em there to feed the buzzards.
Skunks eating from my cat's food dish... I toss 'em over the back fence for the buzzards. Last skunk I killed was gone in less than 2 days. The buzzards were hungry.