Winter Tyres :
The grip provided by winter tyres is not actually to do with a bigger 'tread' as such.
Firstly they're a softer compound rubber. Normal tyres harden up in winter and go a bit plasticy, thus lose traction on cold wet roads. Thus winter tyres are safer when the average temperature gets lower than 7 degrees C. I tend to put them on end of October, and am just toying with the idea of swapping them back now. (might leave it a week or two, the way things have been going!!).
Think about how much importance motor racing teams put into choosing exactly the right compound tyres for racing. Wrong tyre compound and you;re not going to win the race, no matter how good the rest of your car.
When things do get snowy, its the "Sipes', cut into the tyre, which improve the traction massively. These are the little slits you see.
https://en.wikipedia.org/wiki/Siping_(rubber)
Narrow tyres are better as they cut through the snow, rather than wide ones, which 'steam roller' the snow flat.
rally car with winter set up.
4 wheel drive, whilst obviously better, is not the limiting factor. Been all over in the snow this winter with my front wheel drive mondeo, the limiting factor being clearance, i.e. once the snow gets much beyond 8 inches deep, there's are risk of beaching. However a bit of momentum blasted us through a few drifts.
On sheet Ice, not a lot is going to help you bar metal studding.
https://www.youtube.com/watch?v=MkJO0SCFQLg
Makes me chuckle when you see a Big BMW X5 heading out in the snow, with its big fat wide slick tyres. Its like putting on your hat, big coat, gloves etc, then popping on a pair of flip flops to head out for a winter walk. Its going to end in tears.