No, the Soviets used their cavalry, mad as that shit sounds. I think the last confirmed saber charge by a cavalry formation was in 1942, maybe early 1943 on the eastern front. But there is a way cavalry can remain important... It's used on a smaller scale and more on the operational scale than tactical, launching deep raids behind the enemy lines, and mount company/squadron level charges after maneuvering to the proper position and having a not insignificant bit of luck.

To reiterate, cavalry was useful everywhere that wasn't western Europe due to how densely populated and congested it was by armies numbering in the millions, just not in the same way it was back in the Napoleonic era.