The biggest pit fall is removing the anus, many people ring it and pull it across the interior cavity taking a chance on fouling the meat
My preference is to carry a small hatchet or better yet, a foldable pruning saw and split the pelvic girdle, I cut the trachea and pull it all out over the haunches.
Hunt through the viscera and find the liver....even if you hate it some benighted soul will value it, some trim out the bile immediately some after they're home, heart is delicious, lungs an acquired taste, kidneys only if your from England! after the introduction of Prions and Mad Cow, (in deer its called Wasting Disease) I no longer indulge in brain.....but to each his own, the tongue is too slight to really be worth the time. (
Beef tongue is well worth the effort and Elk not so bad either.)
Once the pelvis is broken the carcass will lie open easier and stay open for cooling, add a prop across the chest cavity and you far along the path to cooling the meat in a hurry. Generally I wait to skin the deer until its home and hanging (but always within 4-5 hrs) as the hair slides well and protects the meat.
I dunno if the Boy Scouts in your area are still in the market for the hide ( they used to take them for free, and get them tanned for leather projects, but that seems to have stopped or at least they are not as public about their desire for them.). Its a damned messy job tanning them if you find you like it there a definite market for a tanner anywhere in the country.
Here is a YouTube
video of some proficient butchers explaining choice cuts and tricks of the trade: