In those temps you have to prepare to walk the bike if it develops a mechanical problem. I've tried changing a flat tyre in -20C and even that didn't work out too well (read: at all). Wear sturdy winter boots and carry enough clothes with you.

You may need to flush the rear hub and put some thinner lubricant in there. I've had a freehub freeze during a ride, meaning it's freely coasting in both directions. Had to walk the bike home.

Get good lights. I invested in a dynohub based lighting system, partly due to experience that batteries can be tricky in very cold temperatures.

--J