Be sure to evaluate the overall condition of the animal before deciding to eat it at all. If normal exterior and body weight and internal organs look okay, be sure to observe the internal organs and muscle meat closely. Beware of internal or external patches of discoloration, odd smells, the presence of lots of parasites, areas of putrifaction, strange colored fluids, etcetera.

Then on to the variables of meat spoilage versus acceptable aging: primarily temperature, humidity, and personal taste, as noted by others.

Finally, remember various forms of intentional and unintentional preservation. Intense dry heat may have turned a small animal into jerky, and intense dry cold may have created a corpsicle. You can freeze, cook and can, turn strips into jerky, smoke, salt, pickle, use in pemmican, make into wet or dry sausage / salami, or preserve in some other way for long-term storage before eating.

So, how long? In some cases a very long time. I believe they have enjjoyed eating some wooly mammoth meat found frozen in the tundra that was thousands of years old!