My commute to work was only ~15mins on the bike, and for the first half I was a bit cold, and then the second half I was unzipping my jacket and would even stand outside the office with no jacket of toque or gloves for 3-5 minutes in -40 temps to cool off. The steam coming off me was always fun :)
With a longer ride (my landlord rode 40 mins each way) you stop after about 20 minutes and change layers - usually go for windproof with minimal insulation to prevent overheating/sweating.
side note: i snooped your profile a bit and i'm intrigued by the path you've chosen. i am moving in a similar direction, and no doubt could benefit from referencing your experience...
On my feet I wore thick wool socks, and very well insulated winter boots. They were always hot, even just standing still past -40
For my face I had a toque under my helmet and a big thick merino wool neck warmer that I would pull up until it was right under my eyes - so it covered my ears entirely.
Half way to work I would pull down the neck warmer, unzip my big jacket, etc. in an attempt to not sweat too much.
.. haha, yeah, my path has been a different one, and I'm a thousand times happier than when I sat at a desk. I'm TheRoadChoseMe around the web, and my email is dan @ that .com if you want to get in touch!
Yes, even in -40 and beyond temperatures I rode. In fact, Whitehorse has the highest rate of bike ridership in Canada!