Rock Chuck,
What happens in both deboning warm meat and cooling too quickly (before rigor mortis has come and gone) is the meat cells actually contract in length, which is what makes the meat tough. Cooling too fast, however, doesn't matter UNLESS the meat goes from warm to freezing solid in a few hours.
59F is the breaking point on cold shortening according to what I've read. If meat gets down to 59 too fast, it releases large amounts of calcium that causes the fibers to contract. If they contract, the meat is tough.
My opinion is if it's warm, skin immediately to prevent spoilage. If it's cold, leave the hide on for a couple hours to slow the rate of cooling. How long depends on how cold. Of course how you do anything depends on your situation. Ideal handling is seldom possible.
In the packing plants, they use electric currents to prevent it but I've never been inclined to haul an RV battery around in my pack when hunting elk.
