re: "...resist the urge to get wide tires; the taller and skinnier the tire is , the better the traction in snow will be...."
I couldn't agree more, and I'm sorry I didn't think to add that myself.
More physics

, if interested:
Going in sand and even most consistencies of mud benefit from a wide, "high floatation" sort of tire, as well as lowered air pressure! In contrast, going in snow benefits most from the narrowest tread (and therefore tallest sidewalls, or high apsect ratio). Here's why:
Sand and mud have a generally uniform density through their depths -- because neither sand nor mud (i.e., the water in mud) are compressible. Therefore, the best solution is to stay out of those materials and remain above them. Also, they have a certain amount of resistance to being "pushed around" (for lack of a better term) and the tires' treads can generate some force against them, and in reaction push the car forward.
A broad tire advancing (not stationary) through sand and mud, presents a somewhat harder to sink frontal area -- lowered air pressure also helps, because it increases the area of the contact patch and spreads the car's weight over a larger area, with less pounds per square inch downward pressure pushing the tires into the sand or mud.
Snow, on the other hand, consists of ice crystals that tends to deform due to repeated cycles of compression and melting-refreezing as traffic moves over it. Very quickly, the "snow" pack becomes a material of varying density, loosest on top and densist on the bottom. Thus, there is some advantage to enabling the tread (assuming you've got appropriate snow tire lugs -- and somewhat better*, studs) to reach deep enough to "push" against the deepest, and densist part of the snow pack which best resists the tread and provides a forward reaction. Thus, you "go" better when your tires are pushing against the deep, hard packed snow at the bottom instead of the loosest "fluff" on the top [assuming your snow tires are tall enough to reach it]....
[ * studs are really of greatest advantage on glare ice, not snow, but if the material at the bottom is icy (or the snow is covering ice), it could help a bit.]
... And narrow tires reach deepest, tending to cut through the snow like a "deep V" displacement boat hull rather than a broad, "planing" boat hull that tends to rise above its substrate.
Also, increasing tire pressure helps here, lessening the area of the contact patches and increasing the downward pressure (pounds per square inch), making the tires sink better.
And, in any amount of inevitable sinkage of the tire into the snow as it is rolling forward (not stationary), the front area of the narrow tire is less than the wider tire, and there will be less snow-plow effect and therefore less resistance to advancing through the snow.
How's that?
