Yes! Both sides had a ton of strategic and tactical plans for an eventual war.

Operation Unthinkable: https://en.wikipedia.org/wiki/Operation_Unthinkable

This was a strategic plan for war between the Western Allies and the Soviet Union.

Plan Totality: An Eisenhower-created plan for strategic nuclear war against the USSR

Exercise Swarmer: A wargames scenario involving a Soviet invasion of the mainland United States using a combination of amphibious assaults and paratroops dropped behind the US defensive lines

Operation Dropshot: Another war plan for pre-ICBM nuclear war with the Soviets

Exercise Totskoye: A Soviet plan for offensive operations during an on-going nuclear bombardment of the NATO allies. The stated goal was to find out what would be necessary in the event of using nuclear weapons as a tactical weapon to break through heavily fortified areas (tactical in this case involved nuclear weapons of the same power as Little Boy and Fat Man)

There are tons of others! Check out "Seven Days to the River Rhine", which was a Soviet plan for offensive operations in the event of a total, all-out Soviet invasion of Western Germany, and it starts with the assumption that NATO would launch preliminary nuclear strikes along the Vistula River to prevent Soviet troop movements.

There was also Operation Able Archer, which very nearly led to the beginning of WW3 due to a combination of factors. Firstly was that the Soviets didn't believe NATO when they were informed of military exercises due to the scale and scope of the military equipment and troop strength - to Soviet satellites and spies, the sheer amount of things NATO was using in Able Archer looked very much like a buildup preceding a large-scale, full-strength attack. Secondly was a glitch in a Soviet early warning radar system that gave a false positive of incoming NATO first-strike ICBMs, which was luckily dismissed as a computer error. Thirdly, Able Archer utilized the DEFCON system in a simulated progression from DEFCON 5 to DEFCON 1, which the Soviets interpreted as a serious usage of the system and began making preparations for a full-scale retaliatory nuclear strike as soon as confirmation of incoming ICBMs was received by the Soviet military.

All in all, it is possibly the closest the world ever came to a nuclear holocaust.

And the next year, Reagan didn't learn anything from the experience because he was joking around prior to a speech and made a microphone gaffe in which he stated "My fellow Americans, I've just signed legislation that will outlaw Russia forever. We begin bombing in five minutes." Naturally, the Soviets flipped out over this and took it as a very serious and imminent threat.