Mutually Assured Destruction is a rather late-stage development, not formulated until the 1960s. Prior to that, the USSR did not have the ability to enact "assured destruction" on anything like a mutual scale as the USA could do against it, because it lacked the ability to deliver its nuclear weapons in large numbers over large distances.
In the late 1940s and early 1950s, the USA's nuclear doctrine was pretty unclear — it wasn't at all obvious under what conditions it would use a nuclear weapon and whether that use would be strategic (cities) or tactical (tanks). The US did put in place, by the mid-1950s, a network of bomber bases that could be used to launch attacks against the USSR but, again, the tactics were still being worked out. Most of the US weapon cores were not in the hands of the military and could not be used without being first transferred from a civilian agency.
By the late 1950s, much had changed. Sealed-pit weapons meant that the military/civilian distinction had been mostly eliminated, and the Eisenhower administration had formulated a stated nuclear doctrine: "massive retaliation." The idea was to rely on nuclear weapons as a means of deterring even non-nuclear behavior on behalf of the USSR; it was explicitly a doctrine of non-proportionality (you attack us a little, we attack you a lot).
The difficulty with this proposition was its believability. Would the USA really kill 400 million Soviets and ruinously contaminate Eastern Europe if Soviet tanks showed up in West Berlin? Maybe. Would do they do it if the Soviets rigged the Greek elections? Probably not. Where's the line, then? It felt like a bluff, and the Soviets were good at doing things that were shy of provoking that sort of commitment.
The Eisenhower administration sought to make its use of force more believable by introducing tactical nuclear weapons in quantity. These were smaller weapons that could be used for "limited" nuclear wars — attacking only tank and troop formations, for example, rather than cities and regions. The idea here was not only to help American and NATO forces beat back Soviet tank rushes, but also to make it look like you could have a more subtle form of deterrence: it didn't have to be all or nothing, if you didn't want it to be.
The dangers here were twofold: unauthorized or accidental use of the weapons, and what became called "escalation." On the former, Eisenhower had "pre-delegated" nuclear use in some situations, so that local, on-the-ground officers could make the decision as to whether to initiate nuclear war if they felt sufficiently threatened. This is, in essence, turning over a top-level political decision to the fears of the man-on-the-ground — a recipe for danger. Also, these tactical weapons were hosted in foreign countries, and were often not very adequately secured. (This was a problem with foreign-hosted strategic weapons as well.) If the host nation wanted to become a minor nuclear power, it would only take a little subterfuge. Not ideal. When you combine this with the second problem — escalation — it becomes very acutely dangerous. Escalation theory posits that small nuclear exchanges will likely become large ones very quickly, in particular with the USSR as its smaller stockpile was more vulnerable to first-strike attacks, and thus they would be in a "use it or lose it" situation with regards to their weapons (if they didn't launch first, they would probably not be able to launch second).
After the Cuban Missile Crisis, the Kennedy administration dramatically reduced the number of tactical nuclear weapons stationed abroad, and also mandated that all foreign-hosted (and eventually domestic) American nukes needed to have sophisticated locking systems to avoid unauthorized use.
Additionally, starting in the 1960s, there started a trend of pushing for more nuanced options ("flexibility") when it came to the application of nuclear force, between the two extremes of tactical and strategic. (Early war plans did not allow the US to not nuke China as well, even if they played no part in the aggressive policies of the USSR.) The idea was both that an all-out nuclear attack (a "wargasm" as some wags referred to it) was unlikely to ever be desirable except in the most extreme situations (that is, a failure of deterrence), and that as such it was essentially going to be seen as a bluff. Experiments were done to see if policies could be mutually adopted that would increase the likelihood of national survival should strategic nuclear war happen — McNamara floated the idea of a "no-cities" targeting strategy, for example, where only military bases would be considered valid nuclear targets (a tricky thing, though, is that many military bases are in or near major cities, and destroying hardened military facilities requires surface bursts of the bombs, which creates massive amounts of downwind fallout that affects civilians disproportionately).
This is just an overview of some of the shifts in policy. They become extremely baroque when you get to the period of the 1970s and forward — lots of tiny nuances, sometimes tied to new weapons systems (increased accuracy allows you to decrease yield, and that changes your options a bit), sometimes tied to more political considerations.
For far more detail, see Lawrence Freedman's The Evolution of Nuclear Strategy.
As for the "winning" circumstances, prior to the early 1960s the Soviets were at a distinct disadvantage when it came to nuclear arms and so the idea that you could have a one-sided nuclear war was not entirely implausible. It would mean, however, accepting a ravaged Europe — a high cost. By the 1960s the only way one could envision a nuclear war was at very high American domestic cost (losing a few major cities); by the 1970s the Soviets had capabilities to match the Americans tit-for-tat.