All I know is the narrower the better.. That's why rally cars use amazingly narrow tyres in snow conditions.
But they aren't just for snow.
I tend to put 'winter' tyres on for about 4 months (Dec to Mar) as they give much better grip in snow, but also in the frost.
With the weather we get, it's probably more use in the frost than the snow...but if it wasn't worth doing, I wouldn't have been buying winter wheels and tyres for the last 10 years!
It also saves your nice shiny 18" wheels from the risks of ice caused kerbing.
Rally cars also use studded tyres...but that's not an option!
To be fair, going sidewards at 120 MPH in the snow isn't too high up my proirity list...more actually being able to get up the road outside my house...and that won't be done at speed, or sideways (I hope).