If you look at the two point scenarios that were generally talked about -- general nuclear war, and conventional war in Europe (with the Soviets attacking), I don't see a very clear advantage on either side.
In the general nuclear war scenario, I don't think it's likely that either side would have been able to conduct a first strike without retaliation, at least from say, 1970 onward. By the 70s, that retaliation would have meant severe damage to all of the major cities on both sides, and neither side would have been in a position to invade the other in the aftermath, so the result is essentially a draw with both sides losing.
In the invasion of Western Europe scenario, I think it's hard to say exactly how it would have played out. The Soviets had huge numerical superiority on the ground and in the air. The West had a qualitative advantage. On the ground, I'm not that convinced that the qualitative advantage was as severe as was suggested by Gulf War I. The Iraqi troops were not as well trained as the Soviets, their equipment was inferior export models of Soviet equipment, and engagement ranges in the desert were very long, which magnifies the American advantage. In the air, I think the West would probably have won air superiority, but I'm not convinced that tactical air like A-10s and helicopters would have been very effective with excellent Soviet air defense.
The most likely scenario probably would have been the Soviet advance stalling out somewhere on one side or the other of the Rhine due to a long logistical tail.
Either way, whichever side was losing likely would have resorted to tactical nuclear weapons, and it's difficult to see how this wouldn't escalate into a general nuclear war.