Well since we are all about history here I feel that we should let the facts stand. Each confederate cavalryman was required to acquire his own mount and was paid 40 cents a day for her maintenance and purchase (I say her because stallions are NOT recommended from a cavalry standpoint. They tend to get a bit... frisky and feisty). While this system resulted in a number of loopholes that enabled men to escape duty the overall care of the mounts fell to the soldiers and men having immense equestrian experience could patch up a wound on their mount; not absolutely everyone of course but at least a few in each squadron could.
Ulysses S. Grant was an excellent horseman from his days in West Point was never allowed to ride into battle because he abused a mount, this sums up the Union attitude to mounts quite nicely. Union mounts were, especially in the beginning of the war, god awful. Riders rarely had experience being chosen mainly for their physical stature and despite the pleas of those officers who knew what they were doing a veterinarian corp never sprang up. Massive amounts of mounts were lost to neglect and abuse with inexperienced riders taking the reigns and finding themselves in over their heads.
So if you ask me the superior horsemen (the CSA) should be able to patch up their mounts with a specialized rider. This wont break the game as they ride light horses that can easily be dispatched with a single shot but will highlight their mounted talents and help offset the equipment advantage the Union has in general.