Well, there are places on Earth in which it's snow-covered winter for the majority of the year. Surface transportation still operates.
One trick to transport is that snow (and ice) has a very low coefficient of friction, so sliding is the most practical mode, rather than wheels. Pedestrian transportation is usually skis (sliding on snow) or skates (sliding on ice), the commonality being sliding in the forward direction and not backwards to to the side. Skis distribute weight over snow (as do the less-efficient snowshoes) but skates are better where that's not a concern.
Vehicular traffic usually consists of skis or skates and some sort of gripping propulsion. A sleigh consists of skate-like runners pulled by a draft animal like a horse or dog. Snowmobiles are skis propelled by a gripping belt.
In cities near where I live it's not unusual to drive the same cars and trucks that are used elsewhere, but the tires are specially adapted to snow or ice by using different rubber formulations for better friction at low temperatures, different geometries (thinner tires are better in the snow, for example), and sometimes metal spikes or chains to improve traction on the reduced-friction surfaces.
The other consideration, other than lower friction, is usually visibility. Winters are dark most of the day, and even in the light a blizzard is hard to see in. The driving snow can stare your eyes and lead you off the (invisible) road and completely disorient you. We have specialized headlights on vehicles that are lower than regular headlights (they pick up the relief better) but you can still get quickly disoriented and it's amazing how quickly tracks disappear in a blizzard, and how easy it is to get lost when you can't see more than 1 meter in front of your face. If you're looking at surface transportation in constant blizzard conditions, I think the only practical solution is some sort of rail with heating or constant clearing operations.