The issue of dismounted vs. mounted probably had to do with prevailing needs. I don't claim to know much about the war in the TM, but here's my two cents worth....

In mid-1862 most of the infantry in Arkansas were sent across the Mississippi River with Van Dorn, and Federal cavalry forces operating in the TM were relatively few and inexperienced. During the following two years numbers of Federal cavalry forces had increased considerably, were better armed than most Confederate soldiers, and knew how to fight. Also by that time Confederate foot soldiers (dismounted cavalry and infantry) in the TM were much more numerous than they had been in 1862. New mounted forces were probably intended to counterbalance Federal strength in that arm of service.