Hanging, skinning, and quartering only takes me 1/2 an hour if I have everything ready...which I usually don't.
My general method if it is warmer than 50 is to hang'em. Get the skin/fur started around the legs and head. Then I go to town with a gripper and skinning knife.
Once she is skinned out I will take a little time on pulling the backstraps and catfish tenderloins out. Hose them off and package them with my vacuum sealer. Heck I will eat at least one that day.
Quarter her up, rinse off and refrigerate/cooler the parts immediately. I start picking meat off the ribs and neck. I put them in a seperate bag for commercial made products. I get to the quarters as soon as I have a chance.
I process mine from the roota to the toota. I use our kitchen aid mixer with the grinder/stuffer attachment to make my own sausages, burger, brats, jerky, etc...
I do take some cuttings to a place for some of his trail bologna and hot pepper roll.
This is pretty much exactly how I handle the situation, too... Except for the kitchenaid mixer/grinder... I've got a cabelas grinder. Skinning and quartering a deer is quick and easy, especially when they're still relatively warm. The ones that are a real bitch to skin are the ones that have been hanging for several days in a row.
I've done the chest cavity with ice thing before, but I'm not a big fan of it. It's a last resort measure for me. Think of it this way... How much meat do you obtain from that deer that is directly surrounding the chest cavity? Not very much. Putting ice in the chest cavity isn't very effective at cooling off the hindquarters, and that's where a big portion of the meat comes from. Also, I'm not a fan of leaving the hide on as it hangs. The hide is a natural insulator... designed to KEEP COLD OUT OF THE BODY. The meat cools down slower if the hide is left on the deer.
If you don't have a big refridgerator to store the quarters in, a large cooler works well too. Freeze up some gallon jugs of water, place them in the bottom of a cooler, then put a layer of cardboard over top of them. Lay the deer quarters on top of the cardboard. They cool off quick, without laying in the bottom getting all blood-soaked and slimy.