Hmm, I have had only experience of a few whole carcasses of wild animals(well, not exactly "whole",  but usually deskinned and always minus the head). Those were wild rabbit, wild hare, woodpigeons, wild mallard duck. Those were all rather lean. I've never had the opportunity, though, to get whole carcasses from larger animals like deer or moufflon to see how fatty they were, overall.For various reasons,  most farmers/wild game butchers love to throw away the organs and  sell only the muscle-meats. 

Geoff