More of our Whitefish calls start with ice than with cold. Heavy snowfall that sits on a roof rather than sliding off, combined with any heat escaping into the attic, produces the melt-and-refreeze cycle that builds a dam along the eave. Once the dam is established, meltwater backs up under the shingles and shows up as a stain on a ceiling.
Winter highs here hover in the upper 20s to low 30s with dense cloud cover, and December and January each bring roughly 12 to 16 inches of valley snowfall. That is close to ideal conditions for dam formation on any home with a poorly sealed ceiling plane.
The fix is not roofing. It is sealing the ceiling plane, bringing insulation to full depth all the way out to the perimeter where the dam forms, and keeping the soffit intake working. On homes with complex roof geometry, vaulted ceilings or mechanical equipment in the attic, the better answer is often closed cell foam on the underside of the roof deck, bringing the attic inside the conditioned envelope entirely.