As a year round commuter in the snow belt, I can attest that there are decent studded tires out there. Schwalbe's Marathon Winter is a nice riding tire on pavement, very light snow and ice. I have a 700 x 38(?maybe 42?)c on my commuter. If the snow is more than an inch or two, the tire doesn't have enough nubs to cut through the snow. Nokkian has a reputation of having nice tires with a more nubby texture as well as narrower 700c with minimal studs. My mountain bike has more aggressive tires, but moving that bike through the snow is a lot of work.

The studs make ice insignificant, but, as SheFly puts it well, if there is enough snow on top of the ice, your bike tires won't dig down deep enough for the studs to connect. Likewise, people I know that commute on fat bikes (yep, like the Pugsley) find that if the conditions are mixed snow and ice, that the lack of studs on snow+ice send the fat bikes down.

This year I have the ability to take the bus into work. I've been doing a lot of bus riding. I just don't have the skills for riding when the snow is slightly car trodden with icy packed down sections. Fresh snow I can handle; smooth-ish ice, I can handle, but that in between....I need to take some cyclocross/mountain biking classes or just swallow my pride and take the bus.