I haven’t had access to a walk-in for about 18 years but we’d let them hang, skin on, for about 2 weeks. Had to be careful because sometimes the camp man, partially disabled veteran who lived on the property, would volunteer to process your deer and use it for lodge meals.
I keep my quarters in a large cooler for 7-10 days. Well iced but I keep them in waterproof trash bags/can liners so they stay dry. Soaked meat is unappealing.