It makes sense now, I guess. You don't have enough snowploughs to clear all roads within the same hour (we do, snow can come during night and the ploughs will start really, really early in the morning and clear all roads before people get up), and your drivers education doesn't have enough about driving in such weather. Here, driving on small and poorly maintained roads, in rain, snow, black ice, ice, ice and snow and rain at the same time etc. are major parts of drivers education. Things don't really stop unless an avalanche goes off or something like that.
Do you change your tires? We've got summer tires and winter tires. The winter tires has often got metal spikes on them, making even black ice possible to drive on.
And yeah black ice is pretty common over here, it's everywhere, mostly in the transition between autumn-winter and winter-spring because things freeze, melt and freeze again. If the roads aren't salted that can create pretty bad black ice. So it shows up mostly on deserted roads and less used parking lots, and people walking will encounter it more often than cars and buses (oh and we put tire chains on buses and people often use them on bigger cars).