I live in a country which doesn't have snow, but have recently gone to Europe (Czech Republic), where I could "understand" a bit how these things work. Also, my background is with mountainbike on any sort of offroad terrain, including mud and beach sand.

That being said, I think your most concern would be the grooves/ruts from refrozen snow on roads, much similar to sun-baked mud on some fire-road tracks, but much more slippery, and flotation, much similar to riding on loose gravel or sand (I am speculating a bit).

I can see a lot of studded tires are also slightly pending to the knobby-fatty end of spectrum. With wider tires (no need to be super-wide), you can use lower tire pressures to float better and yet don't get pinch flats. Also, with wide AND knobby tires, you can much more safely ride diagonally through ruts without the danger of your front wheel getting caught and you fall.

So, that's my (also a bit speculative) impressions about effects of tire width, tread-pattern and inflation pressure.

Hope it helps!