I copied this from the artic marathon FAQ:

What shoes should I wear when running?

A pair of trail running shoes will work out best.

What clothes should I wear when running?

A layering system is best, which should incorporate the following:

Upper body – thermal layer, fleece layer and outer windproof shell
Legs – thermal layer and windproof pants
Hands – pair of gloves and mittens
Feet – sock liners and woollen socks
Head – balaclava, facemask, hat, neck gaiter, goggles

Might give you a steer on the correct layering. I have always found the Gore windstopper material really good for preventing the effect of windchill.

It gets pretty cold here in Ottawa too (and not that nice dry prairie cold).

For the coldest days I start with a merino wool base layer, it's light, warm & wicking (wool stays warm when it's wet) and available through Mountain Equipment Co-op. Merino wool socks are great too, they keep your feet warm even if they get wet.

I have a couple of pairs of running pants (looser than tights but snugger than track pants) that are great for cooler spring and fall weather and mild winter days by themselves and with the base layer when it's really cold.

Up top I wear a long sleeve technical jersey (with or without the base layer) and then either a half-zip top or polar fleece depending on the temperature and my regular running shell on top of that for wind resistance.

and of course, a toque and gloves.

For slippery conditions a pair of YakTrax can be a life saver. In general you just need to shorten your stride to avoid landing on your butt.

My current profile picture was taken at the Hypothermic Half in January 2012, IIRC it was around -20C that day with very little wind.

ETA: You should be cool (not cold) when starting your run, you'll warm up quickly enough.

Those are cold temps! I like the layering advice above.

I plan to run every single day this winter and will be layering up as well on the extremely cold days