Dedicated winter tyres may be better but not that I've noticed, the Jazz (on Quadtracs) runs out of ground clearance in snow well before it looses grip. I (& SWMBO) have driven through deep snow, on ice, on refrozen slush in temps down to -20c, and everything in between. Speyside winters can be a bit nippy & severe, 09/10 winter being the winter from hell! The only time when the Jazz was just left in a snow pile was in 2009 as even the tooled up Disco 3 struggled with the depth of snow. Party of the reasoning behind getting Quadtracs was that we'd never get caught out by the first proper snow (can be in October) or the last proper snow (can be in May).
The Jazz backed out of this once I cleared the windows, she was on Quadtrac 2s then.
Mind you, when it was too much for the Jazz it was play time, hopefully beating the plough.