Wide wheels DO NOT out-perform narrow and in some cases (notably in the snow and wet) they can be inferior, the Laws of Friction (i.e. grip) state the area in contact is immaterial (i.e. although a wider wheel has more road contact it makes no difference), all wide wheels achieve is to spread the weight of the vehicle over a wider area, which is undesireable: on snow (because wider wheels sit on the surface, narrow have more of a chance to cut through to a firm substrate) and on a wet road, because the wider wheel is more likely to act like a surfboard and aquaplane, i.e. climb onto the wave of water the tyre is trying to displace during forward momentum.
What does increase tyre grip is the grade of rubber, soft rubber will out-perform hard, but wears quicker.
It's not all theoretical! - I know personally of occasions when the driver has had a white knuckle experience with wide wheels in the snow and wet, but I've bored you enough for now so I'll leave them for the future.
Peg.