What is the date and place for the letter in question? It's difficult to answer without a little more context. One more note - you seem to be making an assumption that because one member of a regiment mentions a horse, then everyone else in that command had one, too. Several assignments for men in service outside the cavalry required either a horse or a mule.

Another point to consider - the Confederate soldier had to provide his own mount. A commander couldn't wave a magic wand, make horses appear and declare his regiment to be mounted. They would have to be acquired from home or taken from nearby civilians, which would be no easy matter since Confederate quartermasters labored constantly to find fresh horses and fodder to fed them. The Army of Tennessee was always short in both areas, and not by small margins.

If the regiment was mounted for any period of time before the Atlanta Campaign, service records of members should include receipts for additional pay for use of privately owned horses.