I thought of a few more cold weather tips for you while preflighting this morning.
Depending on the engine you may be able to turn the prop backwards (safer, and easier to grip the not-so-sharp edge of the prop) or forwards (some engines are damaged by being turned in reverse) through about six revolutions. It breaks up the stickiness of the cold oil, like stirring your ice cream to make a milkshake, I suppose. (You are, of course, using an appropriate oil for the temperature, right?) Check your POH.
The battery doesn't work as well in extreme cold, so if you normally extend electric flaps and check lights before engine start, consider waiting until after start. (If it's not dark enough to see the light reflecting off the ground, arrange with someone else to walk around and give you a thumbs up for functioning lights).
You need more strokes of primer in the cold. Trial and error will determine it for your aircraft. I prime with the accelerator pump (fast strokes of the throttle) and it takes 3 strokes, plus one stroke for every degree below 5C. That's a lot, it's a weird plane. If it's damp and cold you have to get that start on the first try, or you may get frost on the plugs, and then it won't start.
Before engine start, don't forget to close the cabin heat control and ensure that your winter coat isn't blocking access to the fire extinguisher, in case of engine fire.