I tend to disagree with the Cold War analogy. The reason I say this has to do with the difference in the temperaments of those concerned. The Cold War, fortunately for all concerned, stayed "cold" rather than involving the use of both sides' nuclear arsenals (in which case it's unlikely that we would be having this discussion now).
This happened because both sides were deterred by the prospect of being annihilated by the other side's weapons. To put it another way, both sides ultimately cared more about their own survival than about destroying their enemies, and thus maintained coexistance for 40 years in spite of great tensions and large differences in ideology.
What about the situation in Beleriand? Well, Tolkien says that by this point in time Morgoth had become fundamentally a nihilist
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left to his own devices he would only have gone raging on until all was reduced to a formless chaos
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(HoME X). Morgoth would therefore have been perfectly happy with Mutual Assured Destruction, being willing to destroy himself at the same time as the rest of Arda.
As for Fëanor, he was constrained by his Oath. Recall that the exact wording was
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to pursue with vengeance and hatred to the ends of the World...whoso should should hold or take or keep a Silmaril from their possession.
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Note that it wasn't actually to regain the Silmarils, just to attack anyone who stands in the way of their regaining them.
It thus seems unlikely that, had either side possessed the Middle-earth equivalent of weapons of mass destruction, that they would have seen any reason not to use them immediately and indiscriminately, regardless of any collateral damage. The problem (for the elves) is, that this ultimately works towards Morgoth's purpose of the destruction of Arda. Tolkien says that it was for this reason (the collateral damage) that the Valar were unwilling to immediately attack Morgoth when he returned to Middle-earth. Instead they waited 600 years, for Morgoth to expend most of his power fighting the elves. Even so, the War of Wrath caused the destruction of most of Beleriand.