This war wouldn't go in anyone's favour.
North Korea is given aid from the United Nation's and from charities such as the red cross. Going to war would cut these, meaning a large population of North Korea would starve to death.Also North gains nothing expect pride, their army is not big enough to invade. The war would end up being raged on North Korean soil.
Vice versa, China is a major ally to North Korea and if Nato or the UN helped South Korea, trade would come to a halt. This would cause economic instability.
This war will never happen cause China will say no.