These aren't exactly cabins, but they do have woodstoves:
http://www.phillipsbrook.org/ http://www.otloose.com/what_we_do/yurt.htm http://www.math.utah.edu/~eyre/rsbfaq/huts.html
And for the future:
http://www.centralmaine.com/news/sto...hutandtr.shtml
Also, Baxter State Park in Maine has bunkhouses with woodstoves that you can ski into. Lot's of winter regs, though.