I do wish that , whenever discussion turns to winter tyres , all other tyres being referred to , by implication , 'summer tyres' would stop .
The standard tyres that we have all been using for many years always were , and remain to be , designed for general purpose use , all year round .
Yes , specialised winter tyres with different rubber formulations and different tread patterns may give some advantage in certain conditions , just as slicks may give an advantage on a dry track day , but that does not mean that general purpose tyres have suddenly had their use diminished .
As for the other discussion above re tyre sizes vs traction , as the tyre footprint increases for the same weight bearing down on it ( and assuming same coefficient of friction ) , then contact pressure will reduce - hence larger tyres do have a propensity to let go earlier on wet or slippery surfaces , and there can be an advantage in using smaller tyres which will dig in and get a grip where larger tyres would sit on top of snow and slip .
Many ( if not most ) modern cars are 'over-tyred' and at a disadvantage in anything other than dry conditions , as an example , my Diesel C Class has larger tyres than my 5 litre W126 did , and I know which one would keep going in all conditions vs which one would get stuck !