Advances by Bragg and Kirby Smith into Kentucky obliged Federal forces to relinquish much of central Tennessee during the late summer of 1862. Maury County and the surrounding country remained under Confederate control until Rosecrans pressed Southern troops out in late June 1863. Forrest and his command crossed the river into west Tennessee on Nov. 22, 1862, and operated in that part of the state until after the Battle of Murfreesboro.

None of this has much bearing on your question. Ordinarily a Confederate cavalryman was required to furnish his own horse. However, if a horse was lost in service (as all the horses in Gantt's battalion were), the government reimbursed the soldier for the appraised value of the animal. In this case, Confederate quartermasters would've supplied the horses necessary to remount Gantt's cavalrymen.

On Oct. 26, 1862, this battalion was ordered to Meridian MS as part of Col. Simonton's consolidated regiment [O.R. series I, vol. XVII/2, p. 737]. A Federal report written on Dec. 25, 1862 (page 482-83), mentions Confederate remounts coming from Texas. I wouldn't be surprised if the remounts for this battalion came from Texas as well.