With your mention of "washing the deer out", I think that's your most prominent source of spoilage. Unless you have contamination by stomach contents or guts, introducing water to your meat is the fastest source of bacterial growth.
The most critical aspects of meat butchery are keeping the meat DRY and cooling it as quickly as possible. There's no reason to hose out a deer. Gut it, hang it, and quarter it out. No water necessary.