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If the bike is dry when you take it out, and its -35C out, there isnt much moisture around to freeze into the cables.
Until hot brakes melt the snow that's built up on them. I suppose it's unlikely, and that crossers in -10C are more likely to get their brakes hot enough to melt the snow than fatbikers trundling across the ice caps.
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Its never happened to me. I've probably ridden through -20C half a dosen times. So cant say for sure. You get into the habit of moving stuff a lot though. Changing gear back and forth, pumping brakes a bit etc.
Also staying clear of salted roads is a must below -15C. I nearly snapped a leg after road slush refroze, Welding my feet to my pedals. Luckily the base of my shoe snapped instead.
Not if you're careful.
If the bike is dry when you take it out, and its -35C out, there isnt much moisture around to freeze into the cables.
Either will work fine. Especially With a low temp oil. The reason the Alasken crew run cable discs, is that fixing a fault in an hydraulic brake can be near impossible on the go. And at -35C you dont want to get stranded for long faffing around in the middle of the Alasken outback.