Depends how bad it is:
Drizzle or light snow? My shoes can handle them without melting.
Regular rain or snow? I have overshoes or I wear my bluchers (yes, I have Veldt) with Dainite/lub/commando.
Snowstorm? I have no-frill snow boots for that (Columbia).
I'm in NYC so there's much more walking. If you're driving to work, I'm sure overshoes will get you through most foul weather. Although I have nice shoes/boots, I tend to go the cheaper route when...