I was wearing some crappy running shoes before, even during winter, the kind that slipped and squeaked everytime I stepped on snow. I really liked those running shoes even if they were falling apart from years of usage. But I absolutely hated them when I fell on my arse or face after skidding through unshovelled snow. I bought these Doc Martens last year for the exclusive purpose of snow stepping (plus they were on sale!). No more slip-n'-slide for moi!
(I tried finding a link for these shoes, but apparently they're discontinued).