I don’t have the extensive experience that some others will have. In my limited experience, up to around -20C to -30C nothing much happens — the magnification ring, turrets, parallax etc. all become stiffer, but they still turn.
Somewhere near -40C both the mag ring and the parallax side focus would no longer turn. I pulled out my leatherman pliers wrapped in cloth but it felt as if something might break if I were to force them, so I abandoned that idea. I also noticed that I could not activate the illuminated reticle.
I made the mistake of trying to warm the mag ring by breathing on it. Whatever moisture was in my breathe condensed onto the scope and froze, making it worse. The ocular lens also fogged and wouldn’t unfog. All in all it was a disaster. The scope was a Zeiss Conquest V4 so not a cheap scope.