Well, you probably do not know the concept of MAD and nuclear winter. As long as the US is cripple, it will not just sit there. It will make sure to annihilate all other industrialized areas, in order to make sure that the US does not fall victim to a future where she herself is economically crippled, while another industrial nation is entirely intact.
Imagine the scenario where US is crippled and China is annihilated and the rest of the world is untouched. The US will end becoming a prey to those untouched industrial nations: Europe, Russia and Japan. In a way, all China need is the ability to ensure that she can penetrate the US missile defense in a second strike and destroy enough of the US economy to trigger MAD and Nuclear Winter.
Both Russia and the US nuclear doctrine are annihilation. China nuclear doctrine is minimal deterrence. The question is what is minimal deterrence. How many US cities needed to destroy before the US would have a second thought about using its nuclear arsenal. Would the BMD embolden the US to think that it could withstand more nuclear missiles and coming out intact. Would China becoming the primary rival to the US making the US more willing to take losses. We simply do not know.
We do know that 300 warheads are no longer adequate deterrence. Otherwise, China would not have invested and expand its nuclear arsenal for the last few years. In addition, it is obvious China is trying to obtain nuclear triad.
Should China consider nuclear winter as a deterrence. The answer is no because the US doesn't really believe in nuclear winter. China couldn't rely on nuclear winter to deter the US. How many nuclear warheads do China need. How many warheads left after the first strike? For every target without considering BMD, you would need at least three nuclear warheads to ensure total destruction. For every major cities, you have multiple targets. For a large country like the US, 300 warheads simply wouldn't be enough of a deterrence.