Most cars have cheap iron exhaust pipes. That leaves them sensitive to rust. However iron pipes can still last rather long because they dries up when they get warm. But this requires that you drive long enough distances to dry up. If you only occasionally drives a few blocks rust can come quickly.
Light white smoke is normal when engine is cold and in humid conditions. This usually disappears when engine gets warm.
Thick white smoke can be a sign that you're getting water in the engine. If for instance the engine block has cracked cooling water can get into the cylinders. That's baaaad! :-( Let's hope that's not your problem.