On the shortest day of the year, the sun rises (though it does stay low on the horizon) at about 10:30 am and sets about 3:15 pm. Not what I would exactly call "twilight". "Twilight" implies that the sun has set below the horizon and visible light remains. There is still around 5 hours of "daylight"...between sunrise and sunset...on the shortest day of the year in Anchorage.
Today, for example...15 days before the solstice...sunrise is at 0956 and sunset is at 1545 for 5 hrs 49 mins of "day" and 7 hrs 48 mins of "visible light".
So it it hardly "dark", even on the shortest day of the year. You have to get several hundred miles further north to experience that.