He was commissioned a second lieutenant of coastal artillery, and his first service assignment was at Fort H. G. Wright during the years 1915–1916.
Fluent in both French and English (parents were from old New Orleans French lineage), Wogan spent extensive time in France as a staff translator for the Army of Occupation after World War 1.
In 1931, Wogan was posted to Panama as a major of Pack Artillery, and oversaw the first ever aerial deployment of artillery, using army aircraft to transport artillery from one side of the Panama Canal to the other.
In 1939, Wogan transferred service branches once again, this time to the Armored Corps. He eventually rose in rank to major general, commanding the 13th Armored division from 1942 to 1945. On April 15. 1945, Wogan fought a desperate German offensive in the Ruhr Pocket, at a German roadblock near the Autobahn interchange Leverkusen, where he was severely wounded by German rifle fire. He was forced to medically retire as a result of these wounds after a lengthy convalescence in military hospitals.
Wogan retired to his wife's hometown of Asheville, North Carolina, where he spent the remainder of his life as the director of the veterans hospital there. He was active in civic causes until his death in 1968.