Born in Alexandria, Virginia, the son of a preacher, Wheat moved with his family to Louisiana as a young boy. Growing in size to 6 foot, 4 inches tall and weighing 240 pounds, Wheat's physical stature was impressive. He was elected a Lieutenant then later as a Captain in the First Tennessee Mounted Regiment under General Winfield Scott in the Mexican-American War. He left the military due to illness and returned to Louisiana where he was elected a representative of New Orleans to the Louisiana State Legislature in 1848. He was admitted to the bar in 1849.