A month has a second full moon every two or three years. This second full moon in a single month (or "moon-th") can be called a blue moon. The fact that the blue moon occurs on New Year's Eve is rare--it happens once in a blue moon; it won't happen again until 2028.
The Buddha lived in a culture that had a lunar calendar. (We use a solar calendar.) He and the monks and nuns meditated all night long under the full moon, the new moon, and the quarter moons. Today monks and nuns still sit all night on full moon and new moon nights.
During the holidays--the holy days--we are more likely to relax and kick back into mindlessness rather than to pay extra attention to the present moment.
Still, tonight is a good time notice the full moon arcing high in the winter sky--even if we do turn blue with cold while we're gazing.