As a parallel question, how true is the premise of the OP? I know that I and my fellow Americans tend to misunderstand the relative latitudes involved (looking at a map right now, I see that London is farther north than the northernmost point of the United States, for example; Boston is at about the same latitude as Rome; and Miami is at about the same latitude as Cairo).

Is the traditional dress of indigenous Americans significantly different from the traditional dress of Old World people from similar latitudes? My gut tells me Old World people did wear more in those regions at least at the time of contact with the New World, but I don't know anywhere near enough about historical costume to know if my gut feeling has much in common with reality.