Only the Day event and Night event get revealed and discarded immediately.
A small correction to this: the day and night cards do not get discarded, but they get set aside. For these are the only two event cards to remain in play over multiple rounds. Usually the game starts with one of these in play already, and it remains in play until the other one is drawn from the event deck replacing the first one, turning night into day or vice versa.
They do get removed from the event deck though, so don't give you the extra round the other cards give.