Research seems to suggest that at the molecular level, the topmost layer of ice crystals is more active / reactive at warmer temperatures and that the forces of friction from boots and tyres can liquify the ice which is what makes ice more slippery at temperatures around freezing, but less slippery at more extreme low temperatures.

When you are dealing with a vehicle's weight and momentum any ice is a bad thing, a bicycle with studded tyres has a fairly high contact pressure, lower mass, and a fairly low rpm engine and can get much better traction than a vehicle in really icy conditions.