It just seems to be a strange discription (mounted) for an artillery battery.

All artillery was "Mounted" on some sort of carriage, whether it was a fixed position carriage, a field carriage, a pack carriage and so forth.

Another point is that all the men of an artillery battery were also mounted in some way. The normal T.O.E of a battery was 120 men and 150 horses to equipe the limbers, cassion, battery supply and ammunition wagons, and traveling forge, plus the gun crews themselves that usually accompanied the guns of the battery.

So for an artillery battery to be "mounted" would be a normal condition of combat readiness. So why was the special notation in orders that Hart's Battery was "Mounted"?

Most Mountain Howitzers were mounted on a light Praire Carriage, light able to be pulled with a single horse or pair of horses, fast, easy to manuver, wide and stable. While the ammunition that these guns fired was excellant against troops, because of their lack of range (900 yards) it was ineffective against standard size artillery. Therefore it was considered as being obsolete, and would have been a reason that such guns would be religated to a reserve status.

If the word "mounted" was not a mistranscribed word, then a possiblity is that the word "mounted" indicated a type of "flying" battery, simular in makeup to Jeb Stuart's Horse Artillery in the Virginia Theater. Assigned in a reserve status so as to be able to respond quickly to any given area of a battle.