Plenty of polar expeditions on skis that has pushed on in -40C, but no one said anything about that being a pleasant experience...

I've heard the snow-becomes-sand argument plenty times, and I think there is some merit to it, but I don't think skiing becomes totally unpractical. Forget about skis gliding like you see on winter sport TV and think more about it like a long and thin snow shoe that you move horizontal instead of lifting them. That is closer to what you do when skiing through virgin snow anyway, even at higher temps.

But I have to admit limited experience with these things, the coldest I've been skiing was somewhere just below -20C, and with a light wind. Any stop more than 3 minutes would require me to push it for another 15 minutes before I could feel my toes again... it's a pretty itchy feeling knowing any really long stops exposed to the wind would guarantee frostbitten toes unless you've got something warmer to put on.

But the skis on my snowmobile had no trouble making progress in -40C, though... Big, clumpy boots and proper clothing made that a fun experience.