Would you consider purchasing a (luxurious) covered snow-mobile for your winter commute? The vehicle would resemble a small car except that it would have skis (runners) instead of wheels.
In some Canadian cities, snowy conditions mess-up our streets and avenues. Billions are spent anually on snow removal, salting and administering all the labour. Salt damage to our cars and the environment has been estimated at billions more dollars!
Oh and don’t tell me there would be more collisions because of slippery conditions. We manage, as it is, to do lots of slipping and sliding and smashing-up our cars with four wheels below us.
ploughing is for wheeled cars!
there would be a track on the back
and perhaps the car could be made “convertible” in that wheels could be attached for the summer months.

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Of course not. What to do when crossing a street plow. I grew up in Edmonton and the streets are maintained well enough to make practical wheeled vehicles. A snowmobile race of steel passing through the street naked.
Sorry, I cycle, even in the snow. . . . . is more fun!