I'm going to preface this by saying I am 100% in favor of using common sense, and I have always allowed players to damage objects with spells as long as it makes sense. For example, I probably wouldn't let a player "inflict wounds" on a locked door, but I would happily let them "thunderous smite" it.

But in the spirit of this thread, if we're applying a rigidly narrow interpretation of the rules as written, a spell only does what its description says it does. Cone of Cold does not say it damages objects. It says it damages creatures that fail a saving throw.

Yes, Chapter 8 says "Characters can also damage objects with their weapons and spells" - and indeed they can, if they use a suitable spell such as Fire Bolt or Shatter which can damage objects according to its spell description.

Again, that's Rules Lawyer Jesse Pinkman talking, and does not represent my own beliefs or opinions.