Gut that critter right there on the spot and get that chest cavity opened up ASAP and stick a branch in its cavity to open it up. Throw snow or a couple bags of ice in its cavity but get it cooled down. Good quality tasting meat depends on how you handle it from the field to the frezzer, besides as 45-70 said, the gut pile is usually gone by the morning.
Alot of WMA's require that you don't field dress it because local biologist want samples, so also cheque with the regulations also. Bobby