In this corner, the Winter Bike. Studded tires, fenders, powerful brakes, simple drivetrain... the essence of cold-weather velo.
(photo borrowed from Steve F's Zen Biking)
And in this corner, the Taun-Taun. Hairy, horny, and ill-tempered... but just the thing if you're hiding out from the Empire.
(this is not the copyrighted image you're looking for)
So how do these stack up on an extreme winter commute? Well, the Taun-taun tends to rear up and dump you when confronted by hostile traffic (whether of the SUV or pissed-off abominable snowman variety). Advantage: Bicycle.
However, in extreme winter conditions, your vehicle is bound to have a mechanical failure at some point, stranding you in the cold. And when that happens, let's be honest -- you can't cut open a bicycle with your lightsaber and/or Swiss Army knife, pull out its steaming innards, crawl inside, and wait out the storm in cozy-slimy comfort. Advantage: Taun-taun.
Of course, as renowned winter commuter and Taun-taun afficionado Han Solo reminds us, they smell bad -- both inside and out. Advantage: Bicycle.
But let's say you need to make your presence known to other users of the road/tundra. The bike has one of those jingly Pee Wee Herman/Grandma bells. The Taun-taun bleats like an enraged goat. Advantage: Taun-taun.
Looks like it's a dead heat, so you'll just have to test ride them both and choose the one that fits you best. The Cycle's homeowners' association classifies a Taun-taun as a "nuisance pet" (and the thing eats our carpets if we don't lock it in a VERY large kennel while we're at work), so we choose the bicycle.
But we're knitting some very cozy sweaters from the giant hairballs...