The scarf goes on the inside of the coat.
If you put the scarf on the outside, like you think you've seen in TV and movies, it's just decoration. Put it on the inside and it's an insulation layer and it blocks the cold air from blowing down your front. Absolutely game-changing. (Also, have a good coat, but that one seems more obvious to people.)
At my local college there are a lot of people from the Bahamas. They often wear hoodies and sandals with socks in the winter! It can get to -20C here and hoodies just won't cut it and sandals with socks could very quickly mean frost bite.
Yes scarfs are great since necks are a prime spot to loose heat during winter. A scarf or even a hood both together are even better. Long coats too none of these waits level ones get a coat at least past your waist preferably past your butt.
Layers are important more for temperature control. Even a hoodies and some sweaters can be warm if you have enough and one outside with wind protection.
Boots not sneakers to keep warm and the grip. So many people wear sneakers all winter now it blows me away. They're slippery, cold, and they probably cost more than winter boots these days.
I don't know what happened but it is as if this was never a problem at all. And it is not "getting used to the bad thing" I just don't feel bad at all.
Breathing through the nose only helps.
It does get a bit moist after prolonged biking, but not badly, and that's not really against my skin.
The main effect is that there's a little pocket of exhaled warm air, just enough to mix with the next inhalation and help warm it a bit.
I can tie a scarf to be just slightly looser than the gaiter, and the extra space decreases the dampness massively, while still retaining almost all of the warmth.
Hollywood doesn't know what winter is :P