merry Christmas and happy New Year are the commonly ones known by all. In my opinion, merry simply depicts vivacity and optimism. In this sense, it suggests more should be expected in the years ahead. Whereas happy unsophisticatedly demonstrates pleasure, satisfaction, gratification or fulfillment.
You can vividly conclude that merry which means expectation. It ushers individuals into the state of fulfillment, satisfaction and excitement into the present and future. Hence, it is just appropriate to have Merry Christmas and Happy New Year rather than Happy Christmas and Merry New Year.
Additionally, Christmas is commemorated within the last few days to the closure of the year, and it is short lived and enjoyed, while New Year has a lengthy period. It means before the next merriment, you would have been fulfilled, satisfied and willing to gratify the maker of all things for another merry Christmas which places you in high pedestal of expectation before stepping confidently into another new year. -- Rachel Pauline Aikins, Ghana, East Legon