So I'm trying to clear the obligatory snow level, but whenever I spend enough time on the ice to slide against a wall or into a corner, movement becomes so slow that I have to choose between abandoning the mission or literally spending an hour creeping to the other side of the room where I hope to be able to hop off the ice (I say hope because I never bothered).

Is this a bug, or am I just doing something wrong?

I tried setting cycles to the default 20000, 40000 and auto, and in all cases I was still experiencing this bug on the ice. I managed to grenade hop my way off the ice at the end of the level though.

One thing you can do is press Ctrl-F11 or Ctrl-F12 in-game to decrease or increase cycles. If you do this in windowed mode, you can actually see the cycle numbers changing by 1000 cycles each time up at the top bar of the window. This is very helpful in finding the sweet spot of cycle speed for your particular machine, since it's different depending on your specs.

+1 Decreasing the cycles that way worked.
Huge thanks!

Yeah. I found in the end of mission a pair of Ice Shoes with spikes. And after activating them by pressing the F3 or maybe F4 button I then could walk normally on the iced grounds. But it is pretty hard to find the Ice Shoes. They are pretty near the beginning of this mission. I found them just moments before coming to the place where I started this mission. And after that the mission was completed.