Woodward was born in Castleton, Vermont, the son of Edwin C. and Charlotte (Barney) Woodward. He received an appointment to the United States Naval Academy and began his studies there on November 21, 1859. One of several whose academy careers were foreshortened by the war, he served on the sloop , the garrison ship "Island" and the gunboat in the Gulf Blockading Squadrons, including two attacks on and passage of the Confederate batteries at Vicksburg in 1861 and 1862.