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 itself is of 19th century American origin. The earliest example of it in print that I have found is in the Gettysburg newspaper The People’s Press, November 1835:
We are glad to find among the leading Van-ites, at least one man, whose conscience will not permit him to ‘go the whole hog’ in pulling the wool over the people’s eyes
At first sight, the ‘wig’ derivation sounds like a plausible derivation but there must be an element of doubt about it as the wearing of wigs 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 Thomas Jefferson (President between 1801 and 1809), although a wig wearer himself, 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.”
If not the wearing of wigs then what is the derivation of ‘pull the wool over someon’s eyes? Well, we don’t know.
See other phrases that were coined in the USA.