To maintain the proper speedometer calibration when not changing gears, the tire circumference needs to be the same. If you increase the width of the tire, leaving the sidewall height ratio the same, with the same rim size you will have a larger circumference (rim size + ( 2 x sidewall ratio x tread width). If you increase any one of the factors, you will increase the circumference. You need to compensate by decreasing one of the other factors; either rim size or height ratio.
A narrow tire is better in snow because of this:
Take a 3,800 lb T-bird with 60% front and 40% rear weight distribution. That means 2,280 lbs on the front wheels and 1,520 lbs on the rear, translating to 1,140 lbs on either of the front wheels and 760 lbs on either of the rear wheels. If your wheels 215 mm wide, that's a weight distribution of roughly 53 pounds per cm of width on the front and 35 pounds per cm of width in the rear. If you want good grip on snow, the snow needs to be compacted as tightly possible and the best way to compact snow tight is to put as much compacting force on it as possible over a given surface area. The best way to do this, therefore, is to get a narrower tire.
Think about snow shoes - they are large and flat. They distribute the weight over a large surface area and the person walking on them "floats" on top of the snow. Regular shoes dig in far and deep.
that all makes perfect sense now. I really wasn't thinking of the board analogy, but the snow shoe analogy I was, just backwards I guess lol.A narrower tire cuts through the slop better. Wide tires tend to 'float' over snow and slush more. With a wider tire the vehicle weight it distributed across a larger area and thus less pressure between the tire surface and road surface exists (pounds/sq. in). When the botttom number gets bigger the total argument gets smaller (pressure=force/area). More importantly though, the front tires need to be pushed through heavy snow/slush. Think about having to push a board through snow, what would be easier a 1 inch wide board or a 4 inch wide board? In there lies your answer. For snow tires i would get either 215/70/15s or 205/75/15s.