North Korea has had the same (family of) Dictators for a while, but I wouldn't describe it as a stable one. Having mentally unstable people with absolute power in charge is kinda the definition of unstable, actually. As in, they aren't going to be rational actors, who knows what could set them off.
Depressingly, the US somewhat fits the bill too at the moment, but there's at least checks on Trump doing whatever he wants, North Korea doesn't have those checks, he can just have someone killed if they get in his way. Flinched a little when NK responded and talked about a crazy leader that only understands force, because if you took the names out, you'd assume the statement was about NK. *sigh*
Also, you don't get Nuclear Winter from using a nuclear weapon. Or even a couple. So the Pacific will probably be just fine. We've used a couple, and both us and the Russians have tested many more. NW is describing the situation where US and Russia fire ALL of their weapons, and destroy large portions of a couple continents. North Korea doesn't have that kind of firepower, and we don't have the NEED to fire that many to turn South Korea into an island. We're safe on the Nuclear Winter issue at the moment, unless China gets in on this and we go WW3...