Whether December 21 is the first day of winter or the absolute mid-point depends on how you define "winter." Different cultures around the world observe the same astronomical phenomenon, but relate it to the seasons in diffferent ways.
The daylight hours are shortest, and night longest, on Winter Solstice because it's the day when the Earth is tipped with its northern hemisphere as far from the Sun as it gets during the entire year. After this date, the earth's movement as it orbits slowly around the sun brings the northern hemisphere back around to face the light and heat more directly. But, for various reasons including thermal inertia, air and water temperatures on the Earth's surface take a while to catch up with the changing conditions. So the cold season we think of as "winter" lags 4 - 6 weeks behind the astronomical condition that causes it.
