For driving, it depends on the condition of the snow/ice. Is it deep snow, packed snow, solid ice, slush (half melted snow), etc. Generally speaking though, you get winter tires that give better traction on snow/ice and drive slower. The more icy it is, the slower you want to be, because when you try to turn or stop, you may just slide instead. You can also get studded tires that have little spikes in them to give better traction on ice, and chains you can put on/take off when you're going through mixed conditions (ie driving up to the mountains to go skiing, but the roads are dry in the lowlands).

Same idea with walking, you wear boots that have better traction, and walk very carefully. Soft snow isn't much of an issue traction-wise, but exhausting to trudge through if it's deep. If you need traction on ice, you can get spikes that strap to your boots (crampons), they work great.

Dunno about Denmark, but in the US snowshoes used to be a thing, but someone basically made footwear chains for our shoes and boots to give traction, much like the chains we put on our winter tires. They're called Yaktrax