I know there were many strategic and theoretical preparations around the Fulda Gap. There were several serious crises between the USA and the USSR in the Cold War, and I have not been able to find out if in any of them (for example, the Cuban crisis) the Soviet divisions made real preparations to cross the border.
The Soviet Union had devised a plan called “Seven days to the river Rhine” to invade West Germany, Austria, Italy, Denmark and The Benelux nations.
The scenario for the war was NATO launching a nuclear attack on Polish cities in the Vistula river valley area in a first-strike scenario, as well as Czech cities, which would prevent Soviet bloc commanders from sending reinforcements to East Germany to forestall a possible NATO invasion of that country.The plan expected that as many as two million Polish civilians would die in such a war and Polish operational strength would be completely destroyed. A Soviet nuclear counter-strike would be launched against West Germany, Belgium, the Netherlands, and Denmark.
Yes, of course they did
However, there is a big difference between planning and factually invading.
I'm pretty certain that both parties considered on a regular basis invading the other. None of them ever did. Planning to invade/defend something is the favorite pastime of officers, called war gaming. It's a fun hobby (I was a war gamer myself), and even better for officers: they get paid handsomely for it.
I served myself in the army, very often in West Germany smack on the border with East Germany. At that time we worried very much about a possible red invasion. With 'we' I mean most of the population and us serving military in particular.
During my army days I have been often in military war gaming rooms. They war gamed mainly how to defend, but for variety's sake an occasional attack against 'green land' was sometimes played as well. (Never 'red land', as not to offend anyone.) I've never been on the other side of the Iron curtain, but it must have been the same there. Frankly, I would be amazed if they didn't do the same thing.
Looking back with hindsight I doubt very much if the Warsaw-pact could do it. First of all their logistics were pretty bad, to say the least. Another very good reason why no invasion ever came is mutual assured destruction. Okay, so they can conquer large parts of West Germany. The response would be nuclear and even worse: chemical. (I've done the chemical warfare school, believe me: a nuclear attack is a walk in the park compared to a chemical or biological attack.)
What the USSR would have conquered is a poisoned radioactive waste land with many millions of decomposing corpses. (Tom Clancy describes this in vivid detail in his book 'Red Storm Rising')
Yes, they took the possibility into account and yes, they could actually do it long before any US support could of arrived.
But what to do it for ? There was no practical reason to attempt such a thing. It would be illogical to cause heavy losses all across Europe and even affect long-term live sustainability in Europe if everything would end up nuclear.
So they did not made actual preparations/exercises because such an ample action would only come as a possible response to a NATO attack, which they made sure they were ready for.