Perhaps you are having trouble reading Morrow's discharge papers. Being just over the conscript age (35), he was discharged at Little Rock on July 17, 1862, not 1863. The military service file includes a physical description of the man as well as the distance back to Douglas TX and the value of his horse, saddle &c. when enlisted.
If Morrow had been at Arkansas Post, you would expect to see a prisoner-of-war record included in his service file. Apparently he didn't see action as a member of this regiment.