I really like a fur lined parka hoods when it’s cold and windy, I have retro fitted both my military parka and civilian one with fur on the hood. Its cost is not really very high, it’s just a piece of fur not an entire fur coat.

When it is really cold and windy it makes a real difference to be able to hide inside a good fur lined hood. What the fur does is slow down the wind as the air transfers. It effect it helps to create a small micros-climate in front of your face, so you are breathing slightly humidified, slightly warmed air into your lungs. Fur is also great for quickly warming frost nipped skin. As well a good fur lined hood limits overall exposed skin further reducing the chances of frost bit in extreme conditions.
A Good Fur Hat is also a great anti Frostbite Tool. This Picture is me an exercise a few weeks ago teaching Quinche Building and it was -36c plus winds gusting that morning to 30km (i.e. -53c with Wind Chill). You will notice that I had on my Fur Hat, Headover, and only pushed my Hood Back for the Picture. You may also notice the build-up of frost, which is inevitable when active in these conditions. One important point to remember is that often the clothing need to keep oneself warm and comfortable in extreme cold, just gets in the way in mild cold. Wearing it often leads to overheating or build-up of sweat. Dress for conditions, but I recommend the fur hood liner as part of your extreme cold weather clothing.