Well, I run an ebike now but I ran an in-frame two smoker for years and the cold should make your engine run better not worse (cold air = denser)... have you checked your plug recently? You may be running a bit too lean due to that air density, I'd not wrap the motor as it should be heating itself just fine, mine had no issues w/cold at all....Barely Awake; Thanks. You're stiffening my backbone on the issue. I dress much like you describe. And it really does work. The other night was drastically cold. But I was just fine.
My problem in that extreme weather was that my engine started hard and didn't run very well the whole time. But I have options there. I've been pondering some sort of engine wrap that'll hold in it's heat. Also I'm running a 50 cc that is now nearly two years old, with quite a few miles on it. I have a brand new 80cc waiting for this one to die. Maybe it's time to do an engine swap.
But I also ride a good deal off road after dark. And I'm a bit concerned about seeing the ever-changing ice landscape underneath. It might not be really do-able.
But I'll be on two wheels, all the same. It might be pedal and it might be motor.
I did park it indoors overnight, another potential issue is condensation freeze-up I s'pose if you're leaving it outdoors *shrug* My winter warriors lol;