Hayward was born in Willsboro, New York. He served during the Civil War in the Twenty-second Regiment, New York Volunteer Infantry, and in the Fifth Regiment, New York Volunteer Cavalry. He graduated from Fort Edward Collegiate Institute, New York, in 1865. Hayward then studied law in Whitewater, Wisconsin; he was admitted to the bar in 1867 and commenced practice in Nebraska City, Nebraska. He was a member of the state constitutional convention in 1873. He became judge of the district court of Nebraska in 1886. Hayward was elected as a Republican to the United States Senate March 8, 1899, to fill the vacancy in the term beginning March 4, 1899, caused by the failure of the Nebraska Legislature to elect a Senator by the start of the term. He died before qualifying for the seat; he died in Nebraska City on December 5, 1899, and was interred in Wyuka Cemetery.