The cold wind blows, up the stack, and that toilet is tapped directly into the stack.
That's my amateur opinion.
My amateur fix would be to set the float on that toilet so that the water level is low enough not to overflow with a flush, typical "contents" and through the fill cycle.
At least you could get back to bed sooner, and worry about the full, but un-overflowed ceramic fixture, in the daylight hours.
Thanks for the advice. I will wait till it thaws out here to reset it though.