Again according to the CWSSS http://www.itd.nps.gov/cwss/soldiers.htm
Moses H Cross was a private in CO G, 60th TN Mounted Infantry (Crawford's) Also known as the 79th Infantry.
In thesame company was
DM Cross
ED Cross
JL Cross
JS Cross
JT Cross
John Cross
Reese B Cross
Russell B Cross and
SR Cross
Some of these might be the same men
It doesn't list any info on the regiment