He attended Columbian Preparatory School, Washington, D.C.[1] He graduated from the United States Military Academy in the class of 1940 as a Second lieutenant in the cavalry.

[2] He then served in various roles at The Pentagon and then attended National War College from 1958 to 1959 following which he was assigned to the plans division of Supreme Headquarters Allied Powers Europe.

Following an apology, a written admission by the U.S. that Pueblo had been spying, and an assurance that the U.S. would not spy in the future, the North Korean government decided to release the 82 remaining crew members, although the written apology was preceded by an oral statement by Woodward that it was done only to secure the release of the Pueblo crew.

[3] Woodward's statement was: The position of the United States Government with regard to the Pueblo, as consistently expressed in the negotiations at Panmunjom and in public, has been that the ship was not engaged in illegal activity, that there is no convincing evidence that the ship at any time intruded into the territorial waters claimed by North Korea, and that we could not apologize for actions which we did not believe took place.

[5]: 387  On 28 January 1973 Woodward was appointed as the United States representative to the Four-Party Joint Military Commission responsible for implementing the Paris Peace Accords.

On 17 October 1973 Woodward was flying from the Washington D.C. via London to West Germany on an inspection tour when he collapsed on the flight.