I did a trip like that about 20 years ago with "Outward Bound" in the Boundary waters in Minnesota. It was for over 50 adults to determine next steps in your life. We used tarps with a wood stove and used dog teams. I do remember that it got down to -23° one night. I think that Outward Bound has chapters in several states. It may be worth looking into that.

https://www.outwardbound.net/