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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.
Smallfurry-
Good point. I based my guess on reports of cable discs on CX bikes freezing up and an interview with Mike Curiak and riding the Iditarod trail where he briefly discussed his use of hydraulics.
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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.
atk
gbj_tester
I'd guess that cable discs are more prone to freezing (well the cable freezing, rather than the brake itself)