I guess that's a technical question.
Washington WAS a war hereo--but he didn't have to campaign to get elected.
The first candidate to campaign as a "war hero" to win the Presidency was Andrew Jackson--the "hero of the Battle of New Orleans".
Which President inspired the saying "O.K."?
"I say YOU'RE the CUTEST one. No, I say YOU'RE the CUTEST One. And we go on like that from dawn to three."