During freezing periods ice damming can cause water entry into the roof system that is normally waterproof from heavy rain even wind driven rain.
Ice Damming is when there is ice or frozen snow at the lower edge of the roof preventing melting water from draining. The ice causes melted water to extend up the roof under the shingles. Often these are formed due to a warm roof surface melting snow that allows ice to form. The warmth can come from the sun or due to poor roof ventilation or due to poor house insulation.
Roof surfaces that extend past the side of the building will have greater vulnerability due to air flow under the soffit similar to how bridges freeze before the highway freezes. On sloping roofs water can back up under the shingles potentially causing interior water damage. A totally waterproof membrane such as ice and water shield extended sufficiently up the roof surface can reduce the potential for water intrusion on shingled roofs.
As with wind driven rain the water entry may not be readily detected. Ice dams can be removed but should be done by an expert roofer experienced working in winter conditions. On low slope roofs particularly with internal roof drains there can be blockage of the drain system. Consider a low temperature activated roof heating element installed by a licensed electrical contractor.