I can only speak for Switzerland and Germany as I have lived in both for a few years (may have changed in Germany) where it is mandatory to have winter tires on your vehicle on some mountain roads dependent on conditions and announcements made on radio and TV. The police sometimes have a spot check and turn cars away from the roads if they don't have winter tires and also if they are not in good i.e. legal condition.. Even if you venture into the mountains with summer tires when the conditions are bad (ice/snow) and have an accident then your insurance company may well contest any claim you make..
For city driving here in winter you may also find you have problems making claims to your insurance company if you have an accident and you still have your summer tires fitted..
Generally though it is quite common practice for Swiss car owners to have a spare set of winter tires, or as I do- just keep the winter tires on year-round (I only occasionally use the CTT in summer). That way it is less hassle and worry, plus the extra grip in cold snowy conditions is quite remarkable IMHO.
HTH
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