The coldest it's gotten here since I started cycling to work is about -20C.
Really only that cold? That is just under 0°F. I figure it must have been colder at some point. I grew up outside Watertown and I recall it being colder than that at times.
But to the OP, under dressing is the way to and carrying an extra layer or two if you stop. I also bring an extra set of thinner gloves which I can do most repairs while wearing, they are dry and keep my fingers warmer and a easier to handle things.
When it was -5°C the other day I wore two thin merino base layers and my summer heat gear high vis top layer. I only wore tights. When it gets below -5°C I have to start adding more layers. A co-worker commented that I was wearing exactly the same clothes as I was in July, which was true, except the merino and different gloves. When it gets rainy cold and wet that is a different beast and I think more prone to hypothermia and miserable commutes.
Edit: For any other winter than Vancouver I would consider investing in winter clipless boots. I get by here with duct taping vents and holes and wearing shoe covers. Then stuffing the shoes with news print to dry them.