When I took my meat cutter training, we hung the meat for a week to 10 days. This helped to break the muscle tissue down, making the meat more tender. The meat was hung in a walk in cooler with the temperature just above freezing.
Hunting conditions vary considerably due to weather, time of year and available facilities. Some hunters leave the hide on until they can get near the proper facility. One main thing is to remove any damaged meat etc. as soon as the animal is harvested to prevent further spoilage. if flies are a problem, one can lightly cover the meat with pepper, then wrap in cheese cloth. The cheese cloth will still let air filter through. If the animal can not be taken to a butcher shop immediately, hang in the shade out of sunlight.