On snow and ice in low temperature, the rubber compound and the tread design of the winter tires provide more traction than All Weather, then All Season, then summer performance tires, in that order. On snow, wider tires increase float which gives you less traction, think skis and snow boards. That’s why size 225 all season tires are not the best choice to use for snowy winters. 205 or 195 width winter tires would help a lot.
There is physics and there is driving skills to create the dynamic states while driving. The driving skills allow the driver to make use of whatever traction your car/tires has available. The increased traction from a good set of winter tires gives a driver more to work with. Best case is when you have the skills to do all the right things, and with a good set of tires to do it with.