There is a saying in chazal that 1/3 of all the troubles to befall the world will occur in the war of Gog U'Magog.
Is there any hint/allusion in scripture or midrash of an upcoming nuclear war?
There is a verse in Yoel, which may be familiar from the Hagadda (or from learning Navi), which describes the apocalypse. Yoel 3:3-4 (verse 4 included for context):
ג וְנָתַתִּי, מוֹפְתִים, בַּשָּׁמַיִם, וּבָאָרֶץ: דָּם וָאֵשׁ, וְתִימְרוֹת עָשָׁן. ד הַשֶּׁמֶשׁ יֵהָפֵךְ לְחֹשֶׁךְ, וְהַיָּרֵחַ לְדָם--לִפְנֵי, בּוֹא יוֹם יְהוָה, הַגָּדוֹל, וְהַנּוֹרָא.
And I will place signs in the Heavens and the Earth, blood, fire, and timros of smoke. The sun will turn dark, and the moon to blood, before the coming of the great and awesome day of Hashem 1
Metzudas Dovid (ibid) explains the word timros (תמרות) to mean that the smoke will go straight up like a palm tree (תמר).
My father-in-law (who shall remain nameless) wanted to explain the specific choice of a palm tree as the example of something that goes straight up because it spreads out at the top, and the image of the smoke would be like that of a palm tree - a plume going straight up, then blossoming out at the top. Much like a mushroom cloud.
1If anyone wants to translate it as "the day of the great and awesome Hashem" I am fine with that- as far as I know, the modifier is vague.
The best source for an apocalyptic doomsday event (that I have seen) is from an ancient mystical text Sefer Heichalot (http://en.wikipedia.org/wiki/Hekhalot_literature) 5:4-5 and 6:1-2 which is cited by Rabenu Bechaya in Bereishis 44:17 (page 349 Chavel edition)
Among other fascinating and (mind-blowing) novel ideas he writes (translation mine):
A cloud will rise and stand over Rome for 6 months and bring down wet boils on mankind, animal, silver, gold, fruit and metal. Afterwards, another cloud will rise pushing away the [first] cloud and stand in its place for six months and bring down leprosy and skin lesions and an assortment of plagues onto evil Rome to the point that a man will offer his friend "here is Rome [for sale] for a penny" and his friend will respond "I have no interest [even for a penny]."