Yes, this is a black Confederate soldier because Confederate law says so. In fact, these laws indicate that anyone enlisted in the army was a soldier-
"The Congress of the Confederate States of America do enact, When transportation cannot be furnished in kind, the discharged
soldier shall be entitled to receive 10 cents per mile in lieu of all traveling pay, subsistence, forage, and undrawn clothing, from the place of discharge to the place of his enlistment or enrollment, estimating the distance by the shortest mail route, and if there is no mail route, by the shortest practicable route. The foregoing to apply to all
officers, non-commissioned officers, musicians, artificers, farriers, blacksmiths, and privates of volunteers, when disbanded, discharged, or mustered out of service of the Confederate States;" (May 21, 1861)
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