Interestingly though cavalry troops continued to be used through all of WW2.
But only as mounted infantry and scouts. The Crimean War and the Civil War were about the time of the last calvary fighting from horseback on an organized scale.
It is interesting to note how little coverage has been given to the use of horse and mule clear up to WWII, but the great skills of Forrest, Morgan, Sheridan, and Grierson in mounted attacks passed shortly thereafter.