The faster you get the deer gutted and chilled off the better the meat.
Chilled, yes.
you better get him in a freezer within 24 hours MAX!
No!
When you get your deer immediately dress it out and put the ice bag into the body cavity.
No!
i would take your pictures, hang it, skin it and cut it up and put it on ice in freezer chests before i popped the top on my first beer.
No!
Haven't you guys ever heard of "cold shortening"? Icing meat (or taking it to a temperature below freezing) before it has begun to come out of rigor mortis causes cold shortening. This is a temperature-induced contraction of the muscle (meat). It forces liquid (and flavor) out of the meat. {This is the reason commercially slaughtered cattle are electrocuted after being dealt a fatal blow. Depleting the ATP supply in the muscles actually prevents cold shortening, so they can cool and butcher the carcasses immediately after the AC current is applied, without the negative effects.}
Longranger has the right idea:
The idea is to get the carcass cooled and dry not wet.Skinned animals in cool dry air will get a thin dry layer on the outside,this is a good thing,just think cool/cold and dry.
You want to
cool the carcass to 36-44 degrees F, but avoid letting it hard-freeze within 24 hours. And
do not let the muscle come into contact with ice, dry ice, or other frozen objects, if at all possible (that includes being in plastic bags in a cooler).
Cool the carcass! Don't ice it, or start cutting on it, unless you absolutely have to. Cutting into muscle tissue before rigor has passed is just as bad as cold shortening. It causes the chemical reactions to happen at a different rate, and affects the taste, moisture content, and texture of the meat.
If you take your deer on the first day, get it skinned, hang it in the shade, and get the dry skin on it (the dried layer of muscle on the outside). The dry layer prevents maggots from being able to get to the meat. Keep your eye on the carcass. As soon as rigor starts to pass noticeably, bone it out, and get the meat into a 40-ish degree cooler (again, avoid contact with ice for at least 12 more hours). Label bags, as you bone the carcass -- so you, or your processor, can label the packages appropriately after trimming. It would be a shame to see your backstrap and tenderloins end up as hamburger or "rump roast" (likewise, it would suck to open some "backstrap", to find out it's stringy butt meat).
I suffer through the same conditions you have described, every year. Only, I call it the "antelope hunt", rather than "deer hunt"...
One last thing....
Make sure it is legal to bone out an animal in the field, where you're hunting. Some areas don't allow carcasses to be boned out, due to local conditions (such as CWD areas); and some areas don't allow carcasses to be boned out, because the animal has to be inspected by a game warden before it is butchered. Know your regulations, or it might turn into one hellacious ticket.