Cosgrove was born in Tuscarawas County, Ohio[1] to a scholarly family, and one of twelve siblings, most of whom became teachers.

He enlisted in the 14th Ohio Volunteer Infantry of the Union Army at the age of sixteen, and served in the Civil War.

He practiced law and managed 1400 acres of farm land in Washington and Idaho.

[2] A candidate for Republican nomination at several state conventions, Cosgrove won the nomination in the first primary after adoption of a direct primary law, when no candidate won the majority and second-choice votes were added.

After winning the general election, he suffered a heart attack, was too weak to finish his inaugural address, and was granted a leave of absence, earning him the title "Washington's One-Day Governor".