Hunting gal,
Instead of using a rope to drag with, get your self about 10' of 1" wide nylon webbing a sew a loop (like the handle on a dog lesh) at each end...
This is stuff is strong enough to pull an elk out never mind a deer, but rolls up flat so it will fit in a shirt pocket almost...its a lot more comfortable on the hands than rope too...
As for your ATV, i think someones already mentioned a kids sled...if you go to a farm supply place, the sell plastic sleds especially for pulling behind ATV..they are bigger and more durable than the kids ones though..I haveseen the advertised on the Net for between $20 and $30 ago..
Another bit of kit that might might come in handy it what we calling a "Come-along"..its a small hand winch often used for pulling fence wire tight.
Even the smallest will pull a deer no problem and being portable you can use it in all sorts of situations...
The one above is around $35 from cabela's but again visit your local farm supply place..
These things don't carry much rope, so you would need to take say another 50" of light rope as well, but it very handy if kept in the back of the truck...I have actually used one for pulling my truck out of a ditch and also for pulling a knackered ATV onto a truck bed...
Regards,
Pete