For snow tires you want the most narrow, and tallest tire in order to apply the most pressure in the tire's contact patch. That is why BMW only offers(approves) of a
205/50 R17 mounted on a
7j x17 alloy wheel. That is what you want for winter performance.
Widder rubber will give you less PSI(pressure forcing down on your tires(not inflation tire pressure) and pressing the tires into the snow or ice. That will give your tires more "bite" and grip on snow and ice.