A couple of winters ago, I got stuck at the bottom of a gentle incline when there was half a cm of snow. This was in a 1 series with Michelin Pilot Sport tyres (great in the dry, pretty awful in the damp and useless in snow). Winter tyres didn’t just make the car driveable, it made it great.
I bought some winter wheels (complete with tyres, I think they were about £350) and ever since then, I put them on in October and off again in April. Tyre wear is shared between my two sets so it doesn’t actually work out more expensive. I guess I could sell the wheels (if not the tyres) when I’m finished with them. Of course we haven’t had any proper snow since that first winter, c’est la vie.
I live up a hill near Sheffield. So not exactly too far north but we seem to get a fair amount of snow.