I can't stand running on a treadmill, so I've always managed to run outdoors, even in the dead of winter. I need the fresh air going into my lungs.
If it's just snow, and it hasn't turned to ice, the firmly packed snow is usually tacky enough to not slip, if you have a good pair of running shoes with good treads. Even if there's ice on the sides of the road, but also snow, find the snow part of the road and run on that. It is definitely possible.
However, I just spent two weeks in Minnesota for the holidays, and, while my brother and i went out running most mornings, there were a couple of mornings where it really was not
relaxing. They had one day above freezing, and there had been alot of snow, so all of the snow started melting, then re-froze overnight. The roads were like a skating rink. Even in the middle of the roads, which was usually granular snow, because so many cars had passed over, there was a thin layer of ice covering everything. We did the (as my brother calls it) Senior Shuffle until we hit a well-travelled road that was perfectly clear.
But tacky, packed down snow, if it hasn't frozen over with ice, is usually okay to run on. You just have to test it first.