Tyres with large area flat surface profiles are the norm on trucks too, why they also fail to grip early in slippery conditions.
These tyres are necessary for a reasonable life on heavy vehicles, since deep treaded tyres carrying high weights on roads don't last very long due to the lack of support area. Since snow occurs rarely and for so little of the year, it would make no economic sense to use deep tread profiles.
Even if they were used, the many cars using low profile tyres which are equally useless in snow would still bring the roads to a halt.
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I wouldn't have thought that a 'tread' would make any positive difference on a motor vehicle on an icy or powdery snow surface. If you haven't got studs or snow chains (which effectively cut into the surface) what you need is surface area in contact with the road, as the recesses in a tread would either clog up with snow or not contribute materially on an icy surface.
As far as bus tyres are concerned, much the same consideration applies in the rain at the moderate speeds a town bus travels. In general, the tread contributes to sweeping away surface water but doesn't provide grip in itself, and at low speeds it's rather less important.
Where a tread might contribute more directly in terms of grip would be where the surface is soft but sticky (i.e. on mud or damp earth). These conditions don't usually apply in icy conditions with or without snow. Even partly melted snow doesn't have much cohesion, as most of us will have discovered well enough while on foot from time to time.
I can vouch that much more important in general is the composition of the rubber mix from which the tyre is made. A 'soft' mix has better grip in all conditions, as it conforms to the surface with which it is in contact and can be made with a higher stickiness so the coefficient of friction with the road surface is higher. The downside, as Flecc suggested, is the rate of wear. With heavy goods vehicles the tyres have to carry sutained high loads and need to be 'stiff' so as not to flex unduly. In the case of a car tyre more surface area in contact with the road can be designed in by making the tyre more flexible (i.e. a radial carcass) and also wider and low-profile, as usually there isn't so much weight involved.
Motorcycle tyres are these days made from a soft mix because good grip outweighs long life (and the manufacturers don't complain either). Racing tyres are also a very soft mix and have a very short life, and guess what? No tread at all if the race is expected to take place in dry conditions. If the road is dry, you maximise the contact area and therefore maximise the grip. There's no water to clear away as the wheels rotate.
It's only my opinion of course. I haven't got loads of scientific evidence to back it up. There must be something to argue about in here!
Rog.