Hey Lone Gunman. Just a side to correct a minor, but common mistake.
Dragoons were the two original regiments of mounted cavalry and were armed with carbines and sabres as well as the saddle mounted pistols be they single shot percussions or the Colt Dragoon series. Their piping and facing colors were Orange.
The Mounted Rifles were, in effect mounted Infantry, they would ride to a battle, dismount and fight as Infantry/Riflemen keeping the flanks secure. Their main weapon was the M1841 Rifle, a pair of Saddle mounted Pistols and a heavy sabre. Their piping and facing color was green.
Just prior to the Civil War the 1st and 2nd Dragoons and the Mounted Rifles were redesignated as Cavalry and given the Unit designation of 1st, 2nd, and 3rd Cavalry Regiments respectively.
The Original 1st, 2nd, and 3rd Regiments of Cavalry, which were authorized in the late 1850's, were redesignated as the 4th, 5th, and 6th Cavalry resectively. After this all Cavalry Regiments wore Yellow as their facing and piping color.
Hope this is helpful.