Shanks mare for me.
I'm not especially PC, but I bet the methods I've used come close.
In my younger (and stronger) days I'd make a pack out of the gutted deer: Open the hide at the knee on each foreleg, disjoint the bone to make a toggle. Cut the hide through behind each achilles tendon on the hind legs, then stick the toggle from each foreleg through and behind the tendon in each hind leg. Presto. You've turned right and left pairs of legs into "pack straps." Mount it up and pull the head over one of your shoulders, and you're good to go if you don't leave your own guts on the ground somewhere along the way.
When I've been far back without a pack, I've done approximately the same thing with the hide after boning out a deer. Leave the lower forelegs as toggles and poke them through holes in the hide from the hind legs. Use a cord (or I suppose a strap of deer hide) to sew things between into a pack "bag."
Drag em out with a rope if I have time, and these days if it's mostly downhill.
On horseback we split out skinned elk down the middle, cut a hole between the last two ribs and hang that on the saddle horn with a quarter down each side. No prob for two horses and one elk if you're willing to walk out. Works pretty good that way on pack horses too, and helps keep the sides from sliding around without too much lashing. Unless it was a really big deer I'd just hole the hide, hang it across the saddle with the horn in the hole, then mount up and ride out.
Here's a variation on the deer dressing we've developed here in serious bear country. You can do it in under a minute (by the clock) and be dragging your deer out before the bears arrive to investigate the shot: Make a minimum cut, about 6" in the hide, then cut the peritoneum beneath that. Reach up and tear the paunch free just below the diaphram and roll the guts out through the hole. They're soft and a 6" hole is no prob. Now stroke the pellets away from the anus for about 8-10" and cut the large intestine at the top end, then knot the intestine to keep any more pellets from coming out into the cavity.
Now get to scooting, cuzz the bears will be here any minute!!! :rotf: Leave the heart, lungs, diaphram, liver, bladder and rectum for a little while later, at least till you get out into open country where you can keep an eye out for bears.