As I understand it, its more specifically from Gaelic and Welsh sources (mostly from the Gaelic Calan Gaeaf festival).
For example of the possible application of a anti-mask law, the US state of Georgia has an anti-mask law (from 1951) to make it possible to prosecute the KKK who, until that point, had been using anonymity to commit crimes and intimidate witnesses and minorities. It is also very narrowly interpreted according to the Georgia Supreme Court to, as I recall, really only factor into situations where the mask provokes apprehension of intimidation, threats or violence despite not specifying that in the law. The law also makes exceptions for masks for work, gas masks, masks for holidays and masks for theatrical or mardi gras style celebrations.
The law, as its currently interpreted, wouldn't apply to a Muslim woman in a traditional face covering unless she was trying to use anonymity to intimidate others thanks to her anonymity or to intimate violence against others thanks to her anonymity.