Wasn't a ravaged Virginia countryside a primary reason for Lee to cross north of the Potomac?
And, by 1864, the Army of Northern Virginia took great risks by having to send horses [cavalry, artillery, etc] to remote locations in order to be able to graze, or to just merely survive. Many are the stories of the artillery horses being unable to pull the guns as an example of the poor condition of horseflesh serving the needs of that army.
As to the desires of the individual soldiers to be mounted, I'm sure that was pretty much universal. Surely, all the new mounted regiments in the Trans Mississippi organized after mid 1862, were not formed merely to accomodate the preferences of individual soldiers. If that were the case, the entire army would have been mounted, and would have starved itself out in short order.
And, they would have been soundly defeated in combat by smaller forces of trained infantry. That is, if the mounted men were inclined to even take on infantry, rather than using their horses to ride away looking for easier targets.
It is my contention that defeat of the Confederacy, whether inevitable or not, was enabled to a large degree by an ill proportioned preponderance of mounted troops [of all arms]at the expense of an increase in infantry. This applies to all areas of the Confederacy, including the Trans Mississippi.