I have asthma and part of my breathing exercises when the asthma flares up is to strictly breath through my knose. Apparently, although you may feel like you are not getting enough oxygen, breathing through the knose humidifies the air making it easier for your bronchial passages to asorb the oxygen. This is just based on my personal experience.
There used to be a wool hat/balaclava available. It could worn like a normal beanie, or rolled down to form a balaclava. I found wool much better than synthetic. Moisture in breath condenses on whatever you breath through, then freezes. With wool, it condensed and froze on the outside.
Now England doesn't get as cold as it used to. I just use a Buff, pulled up from my neck over mouth and nose.
Theer really are only a very few days in the winter here in southern AZ where "bitter cold" enters the meteorolgy conversation. My ride is at or above 4600 feet.
On those days, I generally wear my garage while pedaling. For the rest of the time I wear layers, set a lower pace and breathe normally, which for me is in through the nose and out through the mouth.
I've been wearing a heat exchanger mask for three winters now (http://www.psolar.com/). I always used to get colds "from" breathing cold air, but since buying the mask that hasn't happened (yes, I know the cold didn't come from the cold air, but from the extra stress that the cold air caused to my immune system's ability to fight off existing germs ...).
The heat exchanger mask even helped me to ride 720 miles of Paris-Brest-Paris with a bad cold that turned into pneumonia by the end. Without the heat exchanger, any hard exertion (like climbing) would make me suck in too much cool air at once, triggering a coughing fit. So any time I would need to ride hard in cool, damp air, I just put the mask on. I still didn't finish PBP in time, because I just couldn't maintain my normal speed. But I'd never have made it anything like as far without the pSolar.