The winter solstice will occur this Tuesday, December 21, at 2338 UTC (6:38 pm EST). This is, of course, when the Earth's Northern Hemisphere has its maximum tilt away from the Sun. It's the shortest day of the year with only 9 hours or so of sunlight (because of the tilt, sunlight doesn't even wrap halfway around the Northern Hemisphere), and the Sun is lowest in the sky (making it cold since it has to heat a larger area).
Just looking at a December full Moon such that it occurs on the solstice in the UTC time zone (time at longitude 000° which runs through Greenwich, England), it's occurred on December 21, 1980 and December 22, 1999. Since it also occurs on December 21, 2010, you can see it's not evenly spaced (19 years and then 11 years). Next time it occurs will be on December 21, 2094, a gap of 84 years. And, even more interesting, a total lunar eclipse will again occur on that date (but visible in Europe and Asia, not in North America like this one).
So what makes this cycle so complicated? It's because the synodic month, the cycle of lunar phases, is 29.530589 days and the tropical year, length of time from December solstice to December solstice is 365.242740 days. They generally, but not exactly, line up every 19 years (19 * 365.242740 days = 6939.61206 days / 29.530589 days = 234.997 which is damn close to 235. In other words, there are almost, but not quite, exactly 235 synodic months in 19 tropical years. It's called the metonic cycle and, despite being named after the ancient Greek astronomer Meton of Athens, this cycle was known even earlier to the ancient cultures of Mesopotamia.
Full Moons on the solstice are not too common, even more uncommon is a total lunar eclipse on the solstice. The last time this happened was December 21, 1638 and the next time will be December 21, 2094. It's truly a once-in-a-lifetime event. Lunar eclipses only occur on the full Moon and only when the Moon lines up with the Sun and Earth. Why not every month? Because the Moon's orbit around the Earth is tilted by about 5° to the plane of the ecliptic. A lunar eclipse only occurs when the Moon is passing up or down through the ecliptic while it's full. This Tuesday morning, three different cycles all line up for us to view.
Of course, and I could have predicted this, the Hudson Valley will be partly cloudy overnight. I'll try to peek out to see what I can see but I'm not optimistic.