Here's the Henry Dixon's I found on the NPS soldiers & sailors.

Henry Dixon - Private, Co. A, 2nd Regiment Georgia Cavalry
Henry Dixon - Private, 65th Regiment Georgia Infantry
Henry B. Dixon - Private, Co. A, 22nd Regiment Georgia Infantry
Henry E. S. Dixon - Private, Co. F, 12th Batt’n Georgia L. Art’y

The one in the 65th seems to be a possible connection. The 65th fought with the army from Chickamauga to Nashville, then was active in North Carolina.