I second mojotex. 100%!
I have a Polaris Sportsman 700 with a Glacier plow system and plowing 12" of snow just isn't going to happen - even 6" is going to be a huge chore. Rule of thumb to keep equipment from being abused is plow every 3". Even if you could clear a 6-12" snowfall it is going to just be pushed off to the edges of the driveway. What do you do with the snow from the next 6-12" snowfall? Or the next? That driveway is going to get very narrow.
I agree with the tractor being the right tool for the job. I would stay away from lighter duty "lawn mower" types and get into an actual tractor. My personal preference would be a Kubota BX or B series. The larger B series would probobly make the most sense if you want to get into ground breaking activities like making gardens or plots with a tiller, digging with a backhoe or using a frontend loader. Moving the snow you go with a snowblower.
Cheap? No. Especially compared to an ATV or UTV. But when it's time to work the job WILL be done. An ATV/UTV and a plow blade would take 4X as long as a snowblower on a B tractor. The tractor will be one path down and one path up - done. Even an ATV/UTV with blower will be up and down probobly 3 times.