I'd keep today's revisions seperate of the original stories. Sometimes modern retcons make more sense but lose some of the power and elan of the Golden Age stories. In the old CAPTAIN AMERICA COMICS, Bucky was shown as the "camp mascot" in uniform. He was too young to legally enlist and the Army knew his age, so he couldn't get in. In the cases where kids lied about their age to enlist, presumably the authorities didn't have information on hand to prevent it, which wouldn't happen in Bucky's case.
Fifteen is a guess, sometimes the Simon & Kirby art made him look considerably younger.