I always quarter my deer up and layer in a cooler with ice. I leave the drain open and prop the cooler up with a brick so when the ice melts it drains out. I usually leave them in there up to a week before I process and freeze.
Also I make sure to keep the cooler topped off with ice and I put a faucet screen in the drain to keep the flys from getting in there.
I will add the stacking method
I usually place the front shoulders. They tend to be shot. Then the hams & neck on top of that the backstraps and tenderloins. That way we don’t have to dig for they. They tend to get fried or grilled quick. 😎
Bone everything, soak in salty ice water 24 hrs. in a large ice chest. Drain, place meat on a rack in ice chest to let it drain. Keep dry as possible. Pour out drainage as needed. Use containerized ice. Leave 5 to 7 days, depending on each deer. Process. Just us, but we put everything into steaks and grindings.