The Snow button works by reducing the amount the throttle valve opens across the accelerator pedal movement range as oppose to normal driving mode. It's supposed to reduce how easy the wheels spin on low friction surfaces by effectively retarding the throttle.
In reality however, the things that are most likely to keep you moving in snow and ice are : more weight in the boot (last year i loaded my boot with 50KG of free weights, it helped a lot) and turning traction off, because on low friction surfaces it's a real hindrance rather than a help.
I think there's been quite a few threads regarding using Snow mode on the motorway to increase MPG.
Edit : Ah, beat me to an explanation, Clossie.