I've ridden in -20 F weather here in Chicago out of necessity, fortunately not too often. I had a hard time keeping my hands warm. If I were doing it again I would definitely go for bar mitts. The other problem I had was that my eyes were watering like crazy and the tears freezing instantly on my eyelashes. You could try ski goggles but they might fog up and then freeze which pretty much makes them useless and it's virtually impossible to do anything about in those temps. I think I would probably wear a pair of safety glasses or wraparounds because they would keep most of the wind out of my eyes but aren't fully enclosed. I'd use heavy socks and well insulated boots. I didn't like wearing a lot of layers because I'd just sweat with the exertion. Thermals and pants, and thermals, a military field jacket liner, and a jacket were enough. I could feel the cold but the warmth of exertion kept me OK. Frostbite is no joke and can happen really fast so keep your ears and nose covered.