Temperature and so the warm organs and body fluids too, ruin meat.
Archery Only 1st deer season in Southern California starts in July. With temperatures in 90F-100F (low to high 30Cs) range inland. Given its Mulies and not Whitetail, and that we can’t bait/feed for tree stand... I don’t partake in the season. Climbing up mountain in The Heat, to stalk on the game, to butcher it on the spot (got to carry water up to rinse) to hauling the meat skin and antlered skull down. Nah.
Even if it’s dead of winter with 0F (-18C) I still prefer field dressing, at least the gut out ASAP. Skinning can wait until out of the sticks.
Birds I leave as is until I get back to the vehicle. Then gut them.
All game goes in cooler with frozen water bottles on bottom and layer of card board above them. Keep it cool, avoid frost bite/freezer burn.