If country A has 100 soldiers while country B has 20 soldiers, even if the cost of war is a 2 to 1 loss in soldiers, war would result in the absolute power of country A.
In a conflict between two countries with nuclear weaponry, the core logic is the same, but the paradigm is different. Nuclear warfare can erase both countries off the face of the earth. This follows from the fact that to combat nuclear attacks, countries started adopting hair-string triggers to destroy the adversary before they can send more warheads their way... except now every country is doing the same thing. In this case, forget the relative nonsense, anyway you cut it, nuclear warfare is not rational for countries because it will end their survival.
My belief is that MAD is sound. And my underlying assumption is that countries tend to think rationally when dealing with international relations. Regardless of leadership, countries do whats best for them an overwhelming majority of the time. Case in point, how often has the U.S. (the bastion of freedom) voluntarily helped countries/people when the U.S.' interests were not directly involved? Also, observe how a seemingly crazy country like North Korea plays the game shrewdly by varying is strategy depending on its adversary.
I agree that there is a threat that nuclear weapons will get in the wrong hands and, in that case, I think its more than probable that disaster would ensue. But the safety and standards for handling infrastructure degradation has improved significantly since the early days of nuclear weapons (when many were lost to the ocean and never recovered) . As for Putin's threats, its nothing a good back and forth of denouncing and condemning can't fix.