Removed. Please see our rules regarding hypothetical questions. You might try checking out /r/historicalwhatif.

Nobody knows, obviously. But the key concept here is called "escalation" — the question of whether increased amounts of power would eventually have to be used. Whole books have been written on this, both during the Cold War and afterwards. Authors vary greatly in their assumptions on this.

Some of it has to do with the technology, as well. Early nuclear weapons were vulnerable to first-strike attacks. So they were in "use it or lose it" scenarios — if you didn't strike first with nukes, you might not be able to strike at all with them. So this put pressures on striking first.

There are many other complex factors, like response times (which got much smaller by the late Cold War — statesmen would have literally minutes to decide whether they wanted to launch their weapons or not), tactical nuclear weapons development (which some thought could be used in lieu of strategic weapons, while others felt they would escalate to strategic weapons quickly), and basic problems of command and control (could the US and USSR successfully negotiate and coordinate their policies in wartime? Remember that during the Cuban Missile Crisis they were reliant on hand-carried civilian telegram services to communicate with each other in DC, and the "hotline" set up after the Crisis was just a regular civilian line, not hardened or expected to survive any kind of conflict).

So we don't know. But I suspect if you could poll the people who were running things at the time, they would guess that any non-nuclear war between the US and USSR would escalate into a nuclear one rather quickly.