People have been trying to forge an arranged marriage between biking and skiing for years, with skibobbing, bikes with tank tracks, and more. Bikeboards, the newest union, utilizes a simple ski design that goes under the front tire, letting the front of the bike float over the snow. Since the Bikeboard compacts the snow, it's easier for the rear tire to keep things moving forward, especially if you use fatbikes, which were designed for snow and sand riding.
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Obviously, the Skiboard renders your front brake useless, but you still have control over the rear — well, as much control as you can have from mechanical brakes in snow. Unless you're in two feet of powder, flats are probably your best bet.