Certainly your "real deal" cowboys (old-time edition) must have had to deal with the cold on a regular basis, especially if they were in the northern states; it don't get much colder than Montana or North Dakota. My impression is many folks were relatively "formal"-looking in their attire: jackets, ties, vests, derby hats ... not all "movie-cowboy"-looking. That said, I think folks just wrapped a wool scarf around their head, tied under the chin ... sort of looked like they had a toothache. Not too "cool" looking, but probably effective. Modern cowboys probably got "hoody" sweatshirts.