Definitely so. Unless you are on the equator, the sun is up for less than 12 hours a day from the autumnal equinox to the spring equinox. The sun will set before 18:00 local solar time. So apart from funkiness with time zones and summer time (which extends a couple of weeks past the autumnal equinox in Aus), yes, roughly half the year.
You're not crazy in the broad sweep of your idea, but actually because the sun isn't a point of light you're also not strictly correct, for example in Singapore the day is always more than 12 hours long.