I've ridden down to -20C or so. I have a dedicated winter bike with studded tyres. In many ways it's not that different from XC skiing. You do need more clothing on your upper torso, because there's less exercise for those muscles.

Enough wool layers, proper winter boots, felt or wool insoles, wool socks, ear flaps + balaclava + maybe skull cap, windproof shell and you're OK way beyond the -20C.

--J