Apparently it also means the hour of the ox . That's from one until three in the morning around the equinoxes, shorter and earlier in the summer, longer and later in the winter. Don't know why as it's native Korean. I guess because it's the first full "hour" of the new "day" . . .
새벽 (dawn) refers to a specific period of time in the morning - just before sunrise. Therefore, to interpret it as "morning", you will need to add a time expression s.a. 2 o'clock; in the early hours of, etc.
새벽 = dawn, daybreak, early hours of the morning
아침 = early morning (breakfast time)
늦은 아침 = late morning
Adding those 3 periods of time,
오전 = morning, a.m.