As a counter-point, I offer the Stony Brook in Lake Shore, MN.
Photo from Steve Kohls, the Brainerd Dispatch
Average overnight temperature in January: -7 F. But it stays open all year round. That particular stream isn't part of Minnesota's winter trout season, so you can't fish it in January, unfortunately.
Maybe the key to finding open water in January this far north is to find spring creeks?
I also suggest this thread would be more appropriate in the Coldwater Fly Fishing subforum.