Interesting question. Haven't been to Fairbanks or Yakutsk (would be fun sometime), but have driven in -20 to -30 F a bunch. My sense is that it's a function of the friction the tires exert on the ice, which is why driving normally and turning, accelerating or decelerating slowly does not make you slide. When it's that cold, you can take more liberties than you can at, say, +20 F. Of course, jamming on the brakes at any temperature will make you slide, even if it's rubber on asphalt without ice in between. The other factor is temperature of your tires, which builds up as you drive and can make a microlayer of water melt even if the ice underneath is cold. Someone else can talk about rubber compounds for snow tires cause I don't know anything about that.
Corollary to that is skiing in very cold temps- XC skiers need different waxes for different temps to achieve that perfect balance of grip vs glide. Wax for +20 when it's -20 and you won't slide much at all.