Tony,
I took a quick look at the Company muster rolls and can only find a few men in Company G that were mounted.
Records of events: Apr 24th; 2 Lts, 4 Sgts, 4 Corpl. and 15 Pvts mounted. May 4th; 1 Sgt and 2 Pvts wounded in an ambush. May 5th engaged the enemy near Raimond,(Raymond) Miss. 1 Sgt, 1 Corpl. and 1 Pvt taken prisoner. May12th dismounted and returned to company.
I know they lost most of their records at Jackson, so more could have been mounted.
MikeT