There are some very good points mentioned here, and some great tips that will come in handy at some point in the future.
Most of my game is harvested during cooler temperatures, but there has been the odd time when it has been important to get that meat into a cooler as soon as possible. I still prefer to get the animal cleaned and skinned, and into the cooler as quickly as possible.
The best thing that I can say other than what has already been mentioned is always use seperate knives for cutting the hair, and working around glands while skinning. The transfer from urine soaked elk hair, or nipped gland residue on your knife to the meat while skinning is probably the biggest thing that will "taint" your meat. And wash those knives thoroughly before using them to cut up any meat.
