That might work up on the high plateau, where the relative humidity is low, and the nights are cold, but down her on the flats, you need to skin the hide off the deer, and wrap it with cheesecloth to keep the meat clean while letting air in to cool the meat. Keep it out of the road dust and pollution to keep the meat tasting something better than exhaust fumes from semis. Get Ice on it ASAP. Ice is sold in 10 lb bags at almost every gas station and stop and puke in the country.
I use garbage bags over the skinned sections of my deer, wrapped in cheesecloth, to keep the meat clean, and give a place to put the bags of ice. I buy the cheesecloth in the Auto section of K=mart, or discount houses, where its sold in 7 yard amounts for polishing wax jobs on car finishes. Seven yards will do more than 4 White tails, so its relatively cheap. The stuff comes in a tube form, rather than as a folded sheet. The tube can be opened up like a sock to slip over the entire length of the deer if you must. I like to remove the hind quarters, wrap them and bag them separately, then both from legs, and wrap them after removing the lower legs, together, in an separage bag, and then wrap the neck and rib cage in a final bag. Removing the legs sections, makes the rest of the deer light enough for one person to carry easily. All go inside my truck or car, and are surrounded by bags of ice, then covered with a tarp, with a bag or two more of ice on top of the tarp( cold air sinks.) I also fold up the hide so the inside is INSIDE and the fur out, then bag it and put a small zip lock bag inside the plastic bag with ice in it, to help keep the hide from spoiling, or attracting flies. It also goes under the tarp during transportation.
I am fond of heart, Liver, and tongue, and those parts go in a separate zip lock bag(s) in a cooler on ice. If I have to stop overnight, I want to be around my own campfire, eating fresh liver and onions, with bacon strips melting over them. The older liver gets the more bitter and tough it gets because the enzymes in the liver continue to break down the sugars in the liver. Fresh liver is sweet, and tender- like prime rib. Heart and tongue need to be slow cooked, and can wait on ice a couple of days before being cooked. Eat the liver, first.