cold and ice can prevent a car door closing or opening, the grease gets thick and sticky and holds the mechanism so it doesn't move freely, but a door should never open while driving, this is extremely dangerous.
Car doors have a two stage lock so even if the door is not closed fully it should still be held securely, if this system is not working, the car should be returned to a main dealer for checking.
Keep on at that garage until you are happy, get it sorted before the warranty expires !