The natural assumption is that this phrase derives from the wearing of woollen wigs, which were fashionable for both men and women in the 16th and 17th centuries.

The phrase is of 19th century American origin. An early example of it in print is from the Milwaukee Daily Sentinel And Gazette, (October 1839), which reads, "And we ask one question that they dare not firmly answer, whether they are not now making a tolerable attempt to pull the wool over the eyes of the people."

The 'wig' derivation is possibly correct but there must be an element of doubt as the practice of wig wearing had largely died out in the USA by the early 19th century. The tradition has continued in Europe where the judiciary of several countries wear wigs in court.

Not so in the USA, where the third president Thomas Jefferson (president, 1801 - 1809, advised the judiciary there, "For Heaven’s sake discard the monstrous wig which makes the English judges look like rats peeping through bunches of oakum."