This is a common misconception. For riding on asphalt or hard ground, narrower tires with knobs or studs are recommended because you want to cut through to asphalt using as much force per unit area possible. This is standard wisdom for basically every kind of winter weather tire, even though it is slightly counterintuitive. More surface area makes it much more likely to float on top of the snow, where you won’t get traction no matter what size the contact patch.