First it should only be hung in a cooler with the hide on.
    The signs to look for: White, red, or green mold inside the cavity. The exposed meat has the color and texture of jerky. The meat feels slimy. The cavity smells like rotten meat.
    If you have to ask yourself it has been hanging to long, most likely it has!
    I still feel that fresh is fresh. I like to do my deer within 2 or 3 days max, and that's having it in a cooler at 34F - 36F.
Dave