I don't know for the woodland Indians but it seems to me that it is a type of ceremony that exists in many places of the continent.
Around Eastern Quebec the Innu have a type of sweatlodge ceremony called matutshan and they had it back in 1633 when father Le Jeune wrote his chronicles, he describes a ceremony taking place inside an Innu winter tent (they were big, having a capacity of about 20 people) in a smaller, low tent that Le Jeune describes as an "oven" , covered with furs, they heat 5 or 6 big rocks that they later put inside the matutshan, then they enter,sing and gently hit the matutshan's sides the whole time they are inside which lasts usually about 3 hours. Back then they used the ceremony to prevent famines by attracting luck for the hunters or for healing purposes. Father Le Jeune is quoted in an Innu author's book, "Croyances et rituels chez les Innus" (beliefs and rituals of the Innu) by Jean Louis Fontaine, on p.56.
Marlene