Scarfs are for people from Toronto and Vancouver who really have no f*#king clue how to dress for Winter. A good lined hood and a touque will do just fine, and if it dips below -30c haul out the dickie.

One can easily survive almost any Southern Canadian Winter (the majority of our population lives within 100km of the US border) with a coat like this:

http://1loveto.com/wp-content/uploads/2014/10/2082M_Black.jpg

Once you go North you may have to re-gear.

These videos are just getting stupid. There is and never was "One" way to dress in each era. Same as today, people dress in a large variety of different ways.
Sometimes we use scarfs, sometimes not, it depends. But I've never seen anyone look as dumb and fake as this woman does while she's wrapped in that scarf and winter gear.

I got through the past three winters (in Candada) wearing only a hoodie. and it dropped below -20c more than I care to admit, and even to -30c a few times.

When I lived further north, I did have a more "appropriate" jacket, for weather down to -40c but I've never owned or worn a jacket that heavy in my life.

Edit: oh, and yes, I own a scarf, just not one that looks a dumb as the ones they use in this video.

Here in Victoria it RARELY gets below freezing. If the sun's out, T-shirts are fine any time of the year out on the course.

FORE!