I live in Kansas City. The winters can be very cold at times but we average in the upper 30's to lower 40's during the day and can get below zero quite often.
I have never had ice inside the house, but I have had a considerable amount of condensation resulting in a mold issue. Last winter I bought a dehumidifier and it eliminated the problem 100%.
Since the interior of the walls are in great condition, I have a strong feeling that any moisture/humidity is leeching up from the moist crawl space (although my hardwood floors are in great condition), even though I have managed to divert the water away from the house.