By March of 1865, The eastern Federal cavalry had ~20,000 Sharps carbines, ~20,000 Spencer carbines and ~10,000 'others', most of which were Burnsides.
Spencer rifles were delivered first, starting in Jan. of 1863 and went initially to cavalry and mounted infantry in the west (Wilders, Minty's Cav., Ohio Sharpshooters and a few others) The exception was Copeland's (later Custer's) 5th Michigan Cav. along with some of the 6th Mich. as well, in the AoP. When carbines started appearing (around Oct. of '63) rifles were rotated out of cavalry units and replaced with carbines.
The Navy contract rifles were actually delivered after Copeland's even though their serial numbers are lower.
Very few Sharps rifles made it into Federal cavalry units, and carbines were in short supply early on due to the Berdan rifle order. However. several states had placed carbine orders ahead of the Federal government, so at least some mounted state troops did show up to the ball well armed.