Many Scandinavian countries require cars to switch over from summer to winter tires and the other way around in spring and in autumn. Some even allow tires with spikes, which damage the roads, but only in winter. Spikes allow you to drive on very icy roads when it is too cold for salt to work. Driving from Sweden into Denmark, they'd actually check your tires at the border in the winter sometimes because they do not want people damaging their roads with their spikes.
Kind of sensible to require cars have proper tires; also from an insurance point of view.
In DFW this year it was -18c one day and two later it was 25c. That isn't normal but every year we have at most one or two periods where there is at most a week of frozen precipitation. The problem is we don't know which month it is going to happen in and it happens suddenly. Climate change made it worse perhaps, but it has been this way for at least decades. I rember waiting in line for santa it was a beautiful 22c, before we got to the front of the line it was -7c.
Many mountainous regions across Europe too, like the French region where I live. Tyres are potentially part of any routine police check. The region is a rather poor one, and many roads are simply not salted at all. With proper winter tyres (and AWD helps too, but it's not as important as tyres), you get through, albeit sometimes with poor elegance.
The amount of snow we get is never anywhere close to those American phenomena I see sometimes in the news, where snow gets half way up your front doors nearly overnight. Seeing that, I'm surprised to read that most people don't use snow tyres in such places : it feels like going against common sense even on an purely individual level.
In places that get a lot of snow we have good snow removal. Thus you don't need snow tires as you aren't driving in it much. You also learn to drive in snow, which mostly means slow down.
And conversely we read about what anyone in the Midwest would consider to be a minor snowstorm and it causes a catastrophe in the South. See for example this article about 3 inches of snow in Atlanta, Georgia.
That makes sense. Then there is still the problem of the cold tarmac, on which summer tyres are said to have poor grip, but that may not be as obvious to the average commuter as a road turned to thick white with two icy ruts to follow. And anyway I'm getting off topic regarding salt :)
This is changing somewhat though. Several of the larger cities in Norway are struggling with poor air quality during winter, so studded tires have either been banned or require you to pay a tax in order to use them. [1]
This doesn't apply everywhere though, and people are require to use common sense and use the tires (and chains) that are best for where they live.
I could see higher rolling resistance leading to poorer fuel efficiency and greater exhaust emissions. Though, I imagine temperature inversions, home heating (particularly via wood), etc. have a much greater impact on Winter air quality.
Kind of sensible to require cars have proper tires; also from an insurance point of view.