Heavy coats are OK for short range journeys, but for rides over 20 mins, its may be worthwhile taking advantage of modern outdoor gear, such as thermal inner layers, and using a thinner windproof outer layer. Do take care that your coat does not obscure the rear light.
For commute riding, as opposed to training, I think its better to avoid sweating in winter. Its cold enough so you can dress to avoid it. You should be fairly cold when you start a ride, but within a few mins you will warm up to "operating temperature".
The cool-down at the end can be problematic. Its not a good idea to stand around in the cold, all sweaty, but building are usually so warm that you will break into a sweat as soon as you enter. I prefer to do a cooldown on the bike, reducing my speed for a few minutes at the end of the ride, and coasting the last section.
You may be able to ride faster with more confidence if you use metal studded tyres, or heavily treaded rubber, rather than a road-going smoothe tyre.
Lots of winter riding advice can be found on icebike.com: home of the winter cyclist.