It being that time of year, there has just been someone asking advice on this on my local web-site ( 5,000' + ski-resort French Alps ). I was very surprised that the overwhelming weight of comments were that cross-climate tyres ( no makes specified ) were pretty useless and would soon see you kissing a tree.
I wouldn't take that as gospel because a lot of the commenters are not particularly informed about car-matters, but it seemed that some were commenting knowledgeably. Unfortunately I can't give you the option of what would be my obviously extremely sensible opinion because I fit Nokian winter-tyres which are truly excellent. Needed now because we had our first 10 cm of snow three days ago and it's been around freezing since then, and obviously the snow is persisting.
There is a big jump up from summer tyres to cross climates for wet and snow conditions -in the UK cross climates will get you out of trouble when the country comes to a halt after 1" of snow settles.
But cross climates arent an alternative to winter tyres -so I dont think they will become commonplace in the heavy snow regions of europe.