It depends on how concerned you are with the ice.

The primary purpose of studs in studded tires is to keep you from falling. On ice, your tires will slide out sideways from under you. If it's the back, most times you can recover. Since we use the front to maintain balance, when the front slides out, you go down fast and hard. And probably in front of a bus. (This is why it's recommended that if you use only one, that you put it on the front.) The "traction", steering, and braking benefits of studded tires are happy side-effects. The studs are really there to keep you upright.

Snowy slush isn't a problem, even for road slicks. I've misjudged the forecast have ridden both 25s and 28s in up to several inches of slush. It gushes out from under the tires, so it's really no problem. Same with up to an inch of light snow. You just use some extra care. On packed snow, or once it begins to clump rather than gush, you'll need some tread. On ice, no amount of tread will help.

Like Juha, I run 700x35 Nokian Hakkapeliitta W106s. I have six winters on them and it looks like they have at least six more left. When buying studded tires for commuting purposes, avoid plain steel studs. You'll likely get only a month or two out of them before you'll need to re-stud. Go with carbide. Nokian and Schwalbe are carbide. Perhaps others too, but I can confirm only those brands.

EDIT: As for cyclocross tires, remember that they're intended for off-road use. I've never seen any with puncture resistance (although some may have it) and their compound is generally soft, meaning they wear quickly on pavement. I have a set of CX tires I use on vacation when I'm 50/50 paved and dirt roads. The rear is nearly worn out at just under 1,000 miles.