The solenoids need to draw quite a bit of power to activate. Sounds to me like the battery was weakened by the cold. It could be current to the door solenoids was attenuated due to the cold affecting your cranking amps. Have your battery checked. I don't think the cold would affect the relays or solenoids themselves. Water/moisture would actually need to get into the doors and freeze up the solenoids which shouldn't happen under normal conditions.

-- John