Thousands, In HS I wrote a paper on this very subject a long time ago. Many VA regiments had more Marylanders than Virginians. Entire VA cavalry troop companies were Maryland men. They had to bring their own horse and if the horse got shot - KIA’d they had a short period of time to replace the horse or join the infantry or artillery, Yuk....
a few thousand perhaps. A cavalry troop in the Confederate Army was about 60-75 men. All Confederate cavalry had to provide their own horses. The South was so short of horses that Confederate artillery pieces were drawn by a four horse hitch.
In the Union Army 6 horses drew a gun.