Mathew Carter (post-war name: Mathew Walker) was born around 1847 in Albemarle County, Virginia. His enslaver, John Coles Carter, was a descendant of Robert "King" Carter, colonial Virginia's wealthiest man. John Coles Carter migrated from Virginia to Missouri in 1852 and owned 126 slaves across multiple properties by the eve of the war. Prior to the war, Mathew Carter worked as a farmer on John Coles Carter's plantation in Pike County, Missouri. Even before he enlisted, Carter suffered from lung issues.

Carter enlisted as a private at the age of 17 on January 18, 1864, in Louisiana, Missouri, and mustered in on January 29 at the Benton Barracks in St. Louis. His service record describes him as 5 feet, 6 inches tall, with black hair, black eyes, and "mulatto" complexion. He served in Company E of the 67th USCT Infantry Regiment. During the winter of 1864-1865, Carter worked in the regimental hospital. Carter himself spent a significant amount of time ill, going in and out of the hospital for months. He did not return to duty with his regiment until March 1865. During this time, he suffered from dysentery, diarrhea, and fever. On July 10, 1865, Carter was discharged from the army due to disability from tuberculosis. He mustered out from Port Hudson, Louisiana.

Following the war, Carter returned to Missouri and worked as a barber. Carter went by the name Mathew Walker, since Walker was his family's name. He married Letha Jackson Carter (Walker) on June 14, 1866, in Louisiana, Missouri. Together, they had four children: Mathew H., born July 28, 1867; William E., born July 16, 1872; and two children whose names are not known. Carter continued to suffer from tuberculosis. He first received a pension of $6 a month, for "chronic diarrhea." Carter eventually succumbed to his chronic tuberculosis, dying on March 12, 1887, in Louisiana, Missouri. His wife Letha's pension began in 1890 and increased to $30 a month by the 1920s.