Since 1793, when The Old Farmer's Almanac began tracking heavenly events and seasonal changes, the Moon has been full on the winter solstice just ten times. The next occurrence will be in 2094. See the chart below.
The rarity of a solstitial full Moon—the average interval is about 19 years—reinforces the Moon's role as a beacon playing on human history. Although our research could not find a correlation between these lunar events and significant historical happenings on similar dates in the past*, the combination of astronomical forces certainly affect the tides.
As astronomer Bob Berman explains, during this time of proxigean tides [unusually high tides due to the Moon's phase and proximity to Earth], coastal flooding could occur if there is one more little extra effect, such as a storm at sea, on-shore winds, or low barometric pressure.
If the solstice night is calm and cloudless, with the full Moon beaming down on a blanket of snow, it will be irresistibly attractive, and electrical illumination—even your car's headlights—may seem superfluous.
* We did find that on the night of December 21, 1866, the Lakota Sioux staged a devastating retaliatory ambush of soldiers in the Wyoming Territory—perhaps planning the attack for that bright night.