For smooth ice you are going down unless you have the studs...
Not necessarily - the Continental Top Contact Winter tires are surprisingly grippy even on smooth ice. You definitely can't expect sudden stops or sharp turns, but you're not going to slide out suddenly because you breathed wrong. Michelin's StarGrip tires are similar. This is because they have very soft, winter-optimised rubber as well as a tread pattern that acts a bit like tiny suction cups.
Studs/spikes aren't the be-all and end-all of winter tires; you also have to consider the rubber compound and how flexible it is at low temperatures. Summer tires, including mountain bike knobbies, have rubber that is most supple in summer temperatures, but will stiffen a lot and *lose* traction when they are cold. You wouldn't notice much difference if it's just hovering around the freezing mark, but at -10C or -20C it is a very different story.
Consider also (in more general thread reply) that snow and ice behave very differently at different temperatures, so one person saying "I can use my summer tires!" in England or California and another saying "I would die without my studded tires!" in Minnesota or Alberta are both correct because the snow/ice they are encountering is genuinely different stuff.
Source: I have ridden year round in Calgary for 12 years (dry cold, snow that tends to be dry and packable; very little ice, but when there is, it's super-polished and absolutely deadly). I've used studs, non-studded winter specific, mildly lugged non-season-specific (FAIL), and a variety of wheel sizes and tire widths.