There is a big difference with non-studded winter tyre and "summer" tyre with M+S mark.
It might feel expensive to have two sets of tyres (summer+winter), but if you want to use your car also at winter conditions (and also avoid collisions) they are worth it and will last several years if used only at winter.
Of course if the winter lasts only few days per year, it is easier just to go for a pub and survive through it
https://www.goodyear.eu/corporate_emea/our-responsibilities/road-safety/winter-tire-recognition.jsp
This ^^^
A true Winter tyre is designed to give optimal grip when the ambient temperature is less than about 7 degrees C. That's the temperature at which the rubber on a summer tyre becomes too hard to grip the 'road' properly. A summer tyre will still work (on tarmac), but a winter will be better below 7, and give reasonable grip on packed snow. However, there are still occasions where a winter isn't enough and chains are required.
Many alpine countries now mandate winter tyres be fitted in the winter months (Swizerland, Italy & Germany but not France). However, the UK doesn't, and given that we only have a few days a year below zero it's probably not worth it for most. I got back from the French alps last week, and during my week there I had to help push several cars & vans up the road outside the apartment. All these had summer tyres and no chains, and were going nowhere fast spinning their wheels on the ice. Cars/vans with winter tyres had no problems.
My hire car also had summer tyres (Lyon charge extra for Winters), so I always buy a cheap set of chains from a supermarket on the way up the mountain (£20 typically). In the past 10 years I've probably had to use chains 5 times, and this was another time. A couple of those times - probably including this one - could have been avoided if I'd had winter tyres, but celery.
Most modern 4WD cars are particularly useless in the snow. They're always fitted with low profile, wide summer tyres which are bad going up hill, and lethal going down hill. Once you get 3 tons of X5 sliding down hill with all 4 wheels locked up it isn't going to end well. You see more X5's and Range rovers off the side of mountain roads than anything else.