Numerous disinformation campaigns were spread about the US during the Cold War by the KGB. Some notable examples include Operation INFEKTION, which attributed the AIDS virus to the US's involvement, as well as the fabrication of the 'nuclear winter' by the KGB in order to slow down US military development.
However, there does not seem to be a large record of the US's disinformation campaigns regarding the Soviet Union. The US CIA was heavily involved in Radio Free Europe; however, there does not seem to be evidence of intentionally spreading fake information through that program.
So the overall question is: What US operations actually caused the spread of disinformation about the Soviets? And if there weren't any, then why did the US not start campaigns like those of the Soviets?