You most likely have a very thin film of ice "gluing" the gasket to the frame. As cold as it is I wouldn't pour any liquid around the door; it might make it worse. If the humidity is low then the hair dryer should work because the moisture will be sucked out into the air rather than melt and refreeze.
Is the lock frozen? If so the deicers you can get at the autoparts store work well there. Some sillicon spray in there and/or some graphite works well.