I killed my 7x7 herd bull during the rut. He ate great. It's all about keeping your hands off the meat while dressing and skinning him and then getting him cooled ASAP. Anyways…. Applies to Antelope as well.
I think it applies to all game meat, get it skinned and cooled as quickly as possible. Don't cut the bladder, intestines, stomach when gutting, obviously and try to keep it off the dirt. We started carrying those free harbor fright tarps that are like 6x7. Put one down and keep the meat clean. Toughest elk was the first one I killed, because it took us 8 hours to get it to the truck in pieces, and we didn't have ice ready.
On our oryx (gemsbok) hunts on WSMR (and near, my first was actually off range, but still on Oscura bombing range area, last one was in the San Adres Wildlife Refuge) we took a lot of bags of ice to stuff inside the animal as soon as we got it into the truck. Some of those depredation hunts were in very, very warm months, even August. Gotta hail them off govt land before you can skin, but you gut them right where they fall. And oryx are by far the most difficult animal I've gutted. It's like they fight you at every turn and every organ attached to the rib cage, thick diaphragm, and all. A mule deer practically guts itself after that. I read that there are wild self-sustaining herds of scimitar oryx here in TX now...
I've never been drawn for pronghorn, but my Dad killed a couple and they were actually better than mule deer. But I hear people form Wyoming and Montana say they are nasty and will not eat them, maybe from the sagebrush?
Our ranking from worst to best is mulie, pronghorn, elk, oryx. Not much for whitetail in NM except those little tiny Coues deer in the Gila we would see sometimes while hunting elk. But they are moving in, and a couple deer we killed about 10 years ago down by the border west of Deming looked like mulie/WT hybrids.