Thing is about "cutting through the snow" argument is, how much cutting are your soft rubbery tyres going to be doing at any width?
The rally argument... "but the rally drivers use narrow tyres in the snow"... yes, they do... coupled WITH MASSIVE F'in studs//spikes to actually cut through the ice proper to the grip beneath.
Overall, I very much doubt your going to notice on a road car the difference between winter wides and winter skinny tyres - I think the biggest noticeable difference is simply in the change of compound... from summer to winter.
I wish the weather would make up its mind and stay cold so that I can benefit from the Winter tyres, I don't need all the double digit sh*t we're set to have next week... where's the fun in that.