I'm not sure if you are specifically looking towards the European countries of WWII, but the Japanese used chemical weapons. Also, chemical weapons are nowhere near as close as dangerous as nuclear weapons. Chemical weapons could be useful for battles, however Nuclear weapons can completely eliminate your enemy. As such why would a country go to war? War is not profitable, as such nuclear weapons are a massive deterrent.

I think you have to consider that the delivery mechanisms for chemical weapons weren't as sophisticated during WW2 as they became later for nuclear weapons during the cold war. The key of MAD as I understand it is that even if you destroy a country's civilian centers, a retaliatory attack will take place, and will have the potential to destroy the attacking country. This was not the case in the era of early chemical weapons; Germany had no mechanism to deliver a payload of chemical weapons to completely destroy the civilian and military centers of America. That capabilities wouldn't be available until the creation of a longe-range jet powered bomber force and then later ICMBs.

Chemical weapons are effective in certain ways, but also quite unwieldy and potentially risky. The deployment of chemical weapons in WWI was practical in part because of the static nature of the Western Front, where you have the luxury of timing your offensives with favourable winds and only (relatively) short distances are covered in offensives. In a mobile, fast moving war they are more awkward to use, although not completely lacking in potential uses. The other major factor to consider is the level of countermeasures available to the opposing army. Gas masks were deployed in large numbers by all the major armies fighting in Europe and gas was, by the end of WWI, much less effective as a weapon than it was upon its initial introduction. While newer and more effective chemical weapons would be developed, mustard gas was by far the most widely produced and stockpiled chemical agent by all powers, and countermeasures had been around since the first world war. The expectation of and preparation for gas attacks in the Commonwealth, Germany and the USSR meant that the expected gains of deployment were marginal.

Chemical weapons were deployed in both the Second Italo-Ethiopian war and in the Second Sino-Japanese War, in both cases against fighting forces that were woefully unprepared to fight modern wars. Even then, they were not employed in every battle, and had marginal overall impacts. As a related note, the Japanese employed biological weapons in 1940 against the Chinese which wound up killing over a thousand of their own soldiers. The general thrust of this all is that fear of reprisals was only part of the story of why chemical weapons were not used in the European theatres. If the Germans believed that the deployment of gas would have caused them to win, they would have deployed it.

Regarding nuclear weapons, there are many differences to chemical agents, the level of destruction wrought being the primary one. While in 1950 it could have been possible for a nuclear war to take place that may resemble something like a conventional conflict with a bit of extra boom, the development of long range rockets and fission-fusion bombs decreased the time it took for weapons to reach targets, reduced the probability of the defenders intercepting the weapon before destination to near-zero (you can shoot down bombers with missiles, but even in 2016 ballistic missile interception is a significant challenge), and increased the yield of weapons from the 15-50 KT range into the 300-20000 KT range. See page five of this document to get an idea of what a potential conflict might be like by the 1960s when mass production of nuclear weapons has really ramped up. The countermeasure for a gas attack in 1940 was a gas mask for front line soldiers. The countermeasures for a nuclear missile attack in 1965 are continuity-of-government contingency plans for use after dozens of major cities have been totally wrecked, all major industry has been destroyed and the country's air has pockets of radioactive poison floating around it.

Once again, I must point out that chemical attacks were not guaranteed to turn a battle in your favour, nor turn a war in your favour. The Germans used it in WWI and it didn't help them overcome the more significant factors of the conflict. The weapons were terrible on a human level, but they were no silver bullet. A nuclear attack beyond the early years of the Cold War on the other hand was guaranteeing a level of destruction that was completely unacceptable, even if you "won" the war.

EDIT:

Now that I reflect on your post I feel like I might have have missed half the question in my response. Why couldn't the USSR and USA have fought a conventional war without atomic escalation? This is kind of complicated and will involve at least partial speculation. But keeping mostly factual, both NATO and Warsaw Pact forces deployed nuclear weapons at the tactical level. The American W54 warhead (10 tons) was deployed near the front lines in Germany, and in the event of a conflict these may have been fired at the advancing WP forces (whom enjoyed a significant numerical advantage throughout the cold war, and thus would be likely on the offensive regardless of who "started" the war). There was a fear that the use of tactical weapons may blur the lines significantly. While it is clear that if the USSR fired missiles at America, America would retaliate (and vice versa), it is not so clear what the appropriate response would be to a small nuclear attack on the Fulda Gap to cover the advance of a Soviet motor rifle division might be. While it may have been possible for a conflict to occur without going strategic-nuclear, many people in both the USSR and USA feared that it was not, and that any conventional attack would lead to a tactical exchange which would then in turn lead to a strategic exchange.

There are a lot of things to unpack here, and some of these questions are not historical ones but political science ones (and will depend on what theory of deterrence you subscribe to).

First, you have the historical case of chemical weapons in WWII. As others have pointed out this was not an absolute ban (the Japanese used them) but in terms of the European war they were avoided. This is as much about historical contingency as anything else and should not be inscribed as some kind of iron law of history or politics. The Allies and Axis that were armed with chemical weapons thought they could prosecute their war aims without using them and that the threat of them being used against them was not worth the benefit. This is deterrence of a sorts, but it is not mutual assured destruction — had one side started using them, it would not have meant the obliteration of either side, it just would have escalated the casualties and forced everyone to wear gas masks. The experience of World War I, which was very recent to those in the European theatre, was that chemical weapons do not provide a decisive victory to either side, but instead just make things more unpleasant for everyone. They are not of the same order of magnitude of destruction as nuclear weapons.

Second, if you are asking, could two nuclear-armed powers go to war without it escalating? This has been a topic of debate since the 1940s. There is no obvious answer. You will find political theorists on both side of the debate. The Cold War game theorist Hermann Kahn, for example, believed that you could have limited warfare, or even limited nuclear warfare, without "escalation" (lots of nuclear war). There are many who believe that it is too dangerous, that the fear that the other nation would attempt a preemptive nuclear attack would be very high, and that fear might lead to misunderstandings (you believe they are escalating when they are not) or a preemptive-preemptive attack. Because the stakes are so high, nobody has been super keen to test out the idea, except in the sense that both the USA and USSR/Russia have been willing to participate in proxy wars, where it was an "open secret" that they were supplying one or another side. With those states, this worked out to be an "allowable" situation.

I am of those historians who do not believe that there is any iron clad "law" that keeps deterrence from escalating, or even that deterrence necessarily "works" all of the time. It is about what individual human leaders and military forces are willing to do or not willing to do. And that can change over time, depending on the people, depending on the technologies available, depending on the situations. There is no reason to expect that these things are fixed in stone, and official strategies have changed over time.

Lastly, I would just note that "deterrence" means more than "mutually assured destruction." MAD is one end of the deterrence spectrum — you destroy me, I destroy you. But there are other, lesser ways to deter. Deterrence ultimately is about being able to prevent someone else from doing something you don't want them to do, by threatening (in some way) something they value. The something you are trying to avoid can be less than all-out nuclear war, and the thing they value can be something less than "the existence of their nation." The example I like to give students is how cats fight off bears. In theory a bear could easily kill a cat. In practice, from the bear's perspective, the cat is a minimal amount of food loaded up with an unpleasant amount of claws. The cat cannot threaten the life of a bear, but it can threaten a bear's eyes, the loss of even one would be very costly to a bear. There are many YouTube videos of bears saying "nope, not worth it" when confronting a cat. The cat has deterred the bear, but it did so without MAD — it could not reasonably inflict equal damage to the bear, but it could inflict enough damage that the bear deemed it not worth their goals. To move the analogy back to nuclear weapons, North Korea is not in a MAD situation with the USA — North Korea lacks the ability to threaten the existence of the USA, but the USA can threaten the existence of North Korea. But North Korea can threaten things the USA values, like Seoul and Tokyo. So the USA is not going to work not to provoke North Korea into a conflict that would hurt those cities, unless it really thinks the alternative is worth the risk.

If you are interested in how nuclear strategy has evolved considerably over time, Freedman's The Evolution of Nuclear Strategy, as its name suggests, is all about this. If you are interested in the various theories (and specific situations) on how the "nuclear taboo" got established and maintained (despite strains), Tannenwald's The Nuclear Taboo is the definitive book on the subject.

Perhaps a question following the original but in a different direction: Do we have accounts of internal discussions within the OKH or OKW debating their(chemical weapons) use and therefore providing us for a context for their lack of deployment?