Everyone seems to agree on the idea that narrow is better for snow, unfortunately the reason for the narrow tire seems to have been lost. The reason why narrow tires are better in the snow is that when a snow tire moves forward it does not actively push the snow out of the way but rather will compress the snow underneath itself and use this compressed snow, which now has ridges ( now you see why tires designed for snow have big chunky tread with corresponding large open areas between the big chunky treads ), to gather traction and move forward. To see this in action take your snow tire to a parking lot with fresh snow, slowly roll the car forward and look at tracks left behind, if you are lucky enough and the snow is deep enough you will notice that the tracks left behind are firm enough to walk on without the ridges collapsing under your weight. This is how a snow tire obtains traction. If a tire is wider the amount of pressure exerted will diminish and the tire will not be able to compress the snow tight enough to gain traction.

In North America we do not usually get the amount and duration of snow to make a pure snow tire useful so most tires for the North American market are designed around the idea of slush, in this case you need a tire that will act very much like a rain tire and push all this slush out of the way to reach the pavement underneath.

But remember the narrower the tire the higher the pressure but also less area over which to obtain traction. In snow it becomes a trade-off, enough pressure to compress the snow given a certain vehicle weight, versus enough surface are to get the traction to move forward.