If one may be allowed to return to the original question .... Two possibilities occur. One is that it's a fossil leftover from the Irish version, in the context of which it might have made better sense.

Second is that cowboys and Western travellers in general sometimes wore an outer garment called a "duster" which was a very thin overcoat designed to protect one's clothes from trail dust, whence the name. I believe dusters were often light colored if not truly white, and generally made of linen so as to be more easily washable.

CC