Make yourself a strap system so you can pull with your shoulders. Hook the deer up so it is pulling from the head and make your ropes short enough that when you pull you are pulling the front shoulders of the deer up off the ground a bit. This makes it easier to get over any logs.
Great way to cripple yourself, trying to drag with your shoulders.
If you gotta drag using a rope or straps, use a band around your hips, so that you are not wrenching your back. It's a bit more efficient, too, as you have fewer moving parts between the load and the ground.
I've dragged deer a fair ways over the years. Longest haul was just about a mile, in just over a foot of snow. You get into a rhythm, and plod along, think about better things and eventually you get there...
Best tool I have for that is a cargo tie-down. One of the ones with the quick release buckle on it. I used to wrap one around my waist like a belt, now I carry it in a pack, usually in the truck or car. I bundle the front feet and the head or antlers, to get them off the ground when dragging, and work from there.
Mostly, these days, I pick my locations so that I can avoid a long drag or carry. And I pick my shots, so that they don't run too far, if I can.
Cheers
Trev