I survived my first winter in western Wisconsin on 700x30 cross tires, used for (short) daily commutes and a bit of recreational riding.
IME, they did well in warmer sludge/slush and light snow, okay on flat snowpack, and poorly on rutted ice. Over the course of about four months of snow and ice, I went down twice. I wouldn't do another winter up here without studded tires, but in warmer regions, the cross tires would be decent.