Don't know who told you this but it's not true...

If using summer tires in the snow then narrower is better.

If using snow tires, wider is better

 

That is totally incorrect......a square set up with minimum contact surface area is best is snow and ice no matter what tire you are using.....summer or winter, the slimmer the better (point of contact with the ground/ snow)

 

It depends on what type of snow driving you're talking about. If you've got super deep snow (several feet) than you want a super wide tire that's aired waaaay down; just a few psi. This way you'll "float" on top of the snow and maintain traction. You'll find this setup on Arctic Trucks:



However, for those of us on unplowed roads (up to 2' of snow) you'll want a more narrow tires which will more easily dig down to the pavement for traction.

 

to move a car on snow/ice you need resistance, wider gives more resistance.
narrow = more weight per sq/inch

For summer tires in snow you are correct but not snowtires in snow