Yeah, I can imagine the skylight issue on a cold Ohio morn. How deep are the SIPS?
A possible approach in addition to a properly sized fan could be sliding covers for the skylights. They make units that might mitigate the amount of moist air entering the skylight well in the first place. Not sure how tall your ceilings are but Mom has these covers on her skylights that are ~14-16' high that she is able to open and close with a provided collapsible wand thingie. Not the most elegant solution but I don't see any easy answers for this problem.
Besides you could close it during the start of winter and leave it closed all season. You won't be missing any of the light as your skylight is covered with snow anyway

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