The only person who will ever start WWIII will be a person who loathes the entire human race who, through some unknown method, came to be in a position of high-power.
When you launch a nuke you aren't just going to get nukes back from who you fired it at, you're going to get nukes from everyone who considers you a threat and then everyone who considers the people who consider you a threat to be a threat to them will fire nukes at those guys and so on, so forth until every single nation on the planet has at least one nuclear missile about to hit them and destroy them.
Mutually assured destruction is not something that exists purely between the two people having a cold war, mutually assured destruction is something which now exists between every single nation on the face of this planet, regardless of alliance, size, politics or culture, to launch a nuke is to guarantee the destruction of the entire human race, so it'd take a true misogynist to even consider doing it.
That's just my opinion, though