I would add the following: "Dismounted" was an official state (i.e. officially ordered by higher command) of being for a former officially designated cavalry or mounted infantry/rifles regiment or battalion. For example, a private might belong to Company C of the 20th Texas Cavalry (dismounted).

It was almost always associated with Confederate troops for obvious reasons, although some Union commands suffered such fate. The main difference is that Confederate troops owned their own horses, whereas, Union troopers did not. No Texan would volunteer to provide his horse to pull artillery. It would be a sure death sentence to his prized possession.