Deer isn't beef - and any aging past 3 days is probably not helping the meat quality any. I field dress right away and usually skin and quarter the next day - unless temps are 50 or above - then I do it right away (usually <50s is not a problem for me). For me ANY meat compromised by a gut shot gets tossed. We usually have more meat than we know what to do with and a water rinse isnt enough to ensure cleanliness for meat in contact with the body cavity. That said - even a gut shot deer - 95%+ of the meat never in contact with the inside of a deer. Just be consistent and smart - and the meat is fine.
If feel that if you like to age your meat - age it after you take it out of the freezer - I usually have sub 32 degrees when I butcher -so i take my time and may take 4-5 days to process - but I have no problem butchering the same day and aging after it comes out of the freezer for choice cuts.
FH