a state of enjoyable exuberance; playful fun
Gaiety and fun
- her eyes sparkled with merriment
Hap"pi*ness, n. [From Happy.]
1. Good luck; good fortune; prosperity.
- All happiness bechance to thee in Milan! Shak.
Merriment is having some good fun, while happiness is a much broader term, relating to overall well-being with all necessities of life, and so on.
Christmas is a time of celebration and therefore a 'Merry Christmas' would be appropriate. A new year, as in 'Happy New Year', on other hand, extends over a whole year (and further on) and as such the sense of good luck, good fortune and prosperity provided by Happy would be appropriate.