Shoot, where I come from, that called a road!
What you have to consider is that depending on the width of the machine you'll be using, you might need to make as many as five or more passes to get the driveway cleared. That works out to almost a mile. Now, depending on depth and type of snow, your speed will vary. I have a driveway that's one tenth of the length of yours but maybe twice as wide. On a good day, with a damned good machine (Simplicity 9.5 h.p. 28" wide), it will take anywhere from half an hour to 45 minutes to clear four to six inches of average snow. So, extrapolating that to your requirements would mean that you will need approx. five times as much time to do your driveway. That works out to 2.5 to four hours to do the job with an equivalent machine under decent working conditions with no break downs. Personally, a walk behind would not be my choice. If you have a four wheel drive ATV, I'd look at a self powered snow thrower for it in preference to a walk behind. If all goes well, it will be much easier and quicker. If you don't have an ATV, the costs for it and a thrower attachment will probably put you in the $10000.00 to $15000.00 range if you buy new, decent equipment. If you have no other use for the ATV, that would be the wrong way to go. You'd be better off buying a good quality John Deer or Kubota yard tractor (preferably diesel) with power take off for a hydraulically controlled snow thrower. In summer you can use the same machine for cutting grass and other utility work. Remember that either the ATV or tractor will leave you shoveling paths and areas too narrow or tight to get at with the bigger machines. A small used walk behind would be good for those places.
Bottom line: No walk behind. If you hunt, fish and like to ride ATVs - go that route. If not, get yourself a good quality, powerful, yard tractor. Good luck.