If WWII is any indication, if a war were to break out with a nuclear-armed state, it would end abruptly. The bombed state(s) would either surrender in the face of certain destruction after the first bomb or two fell, or their military capacity would be so devastated by the strikes that they would be unable to mount an effective campaign.
Couple the brevity of a nuclear war with the higher number of potential combatants and civilians that would be killed in a conventional shooting/firebombing war, and the proportionally higher power of conventional weapons than in WWII, and it's not at all clear that nuclear weapons would increase the overall destructiveness of a major war.
It is clear, however, that major powers are loath to start a potential WWIII because of nuclear weapons, thus saving tens or hundreds of millions of lives. That's what the Cold War was about.