That is true. Whitteny Lane for example. But what was the normal action? Confederate Cavalry (in Arkansas) generally lacked proper mounts and equipment to be considered as functional Cavalry. And it was not confined to just the western trans mississippi arena, for example Forrest cavalry in Tennessee and Kentucky, and Buford's Cavalry at Gettysburg.

At the Battle of Branchville, Union General Powell Clayton engaged the confederate scouts and skirmisher using his Kansas and Indiana Cavalry dismount until the confederates withdrew then he pursued on horse and reengaged again as dismounted Cavalry. an engagement that lasted over 5 hours, in which his forces discharged 20,000 round of small arms ammunition.

As is always said that there are always exception to any rule, but in Arkansas the tactical situation usually favored fighting on foot in my opinion.