If you just moved to a northern climate and have been saying this isn't that bad, then this is a bit of a wake-up call to make sure you are ready for winter. I still do recommend that you keep one of those shiny silver mylar survival blankets in your car. It works not only for warmth but also to put outside the car if you are off road and need to be spotted. Keep a week's worth of good at home that doesn't need electricity to prepare. Power outages in extreme cold are a pain.
People in cold climate know to always have a full set of outdoor clothes in the car, either wearing them or in a bag even for shorter drives. You don’t want to be the guy who freezes to death after not bothering to put on a jacket since you are only picking up a pizza in the next village 3 miles away and then freezing to death because your car broke down.
Well, the one I bought works damn well for heat and had one huge advantage over wool. I can bungee cord it to my car and be very, very visible to any search going on to find me.
I would hope people going out in winter also have proper coats and pants, but extra blankets as well a proper survival kit is a very good thing. Small grain shovels are also quite nice.
USA since a lot of commuting, but I think safety is pretty universal. Depending on infrastructure in any place the climate can kill you might not be a good idea.