Seymour was the third child born to Seymour and Dinah Baxter. He was born in Canada and came to the United States with his family when he was eight years old.
According to the 1860 U.S. census, he lived with his parents and nine siblings on the family farm in Lorraine, Jefferson County, New York.
On July 17, 1862 Seymour enlisted as a private in the Union Army, Company E, 2nd Heavy Artillery Regiment New York.
He was captured a little more than a month later by the confederates at Sudley Church, Virginia (near Manassas). He was released on August 28, 1862, but went on to fight and died on the battlefield of Petersburg, Virginia on June 18, 1864.