Historic Fantasy Questions

There is no way to answer that question with any accuracy. A medieval setting (assuming to mean middle ages in europe) spans a 1,000 year period and a continent ranging from Scandinavia to southern Italy. Each time period and location will have a different answer. Also, the type of animal will make a difference.

In general, salting, drying and smoking (usually using two or 3 of those methods) lets you preserve meat close enough to indefinintely to not matter. A traditional ham (like serano or parmaham) can easily be cured for 15 months before you start eating it. Most of these techniques would have been known in the middle ages (though perhaps not fully understood from a scientific point of view). Though, which technique was used would depend on the region, with the south going more towards salting and drying and the north more towards salting and smoking.

For unprepared meat there's a few vairables. Temperature is the big one. If it's a happy 30C then you are looking at a much shorter time than if it's below freezing. Then, it matters if the animal is intact or if it's slaughtered. Different pieces of meat spoil at different rates. Intestines and organs spoil fast. Muscle tissue not so much. When dry aging, you can hang half a cow at a few degrees above zero (C) for a couple of weeks if you control the environment well enough, but you don't want to try this with a cows intestines. Then of course, humidity also plays a role and so on.

If you're talking about finding a dead animal in the forest then I would go for half a day to a day, depending on the temperature.

 

There is also pickling [using acid preserve the meat], although the contents are usually cured in some way first. Pickled pigs trotter is an acquired taste but rather nice.
And then there are the strange things that people do fermenting meat, especially fish for some reason...