I had this problem about twenty years ago at my business. The solution was an electric driveway mat covering twenty feet of driveway near the bottom. Having it at the bottom allows you to brake to a stop on dry pavement. It also gives you the chance to get some speed to carry you up the driveway.
Electronic sensor detects the snow and turns mat on at the beginning of a storm.
The mat is cheap but install will cost you. However it will be a lot cheaper than buying a tractor. And it will work MUCH better.
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