"Merry Christmas" is a fixed greeting in American English.
In the UK the greeting "Happy Christmas" has become more customary. The word 'Merry' was originally used back in 1565, when it refered to the merrymaking of the alcoholic sort. It has changed over recent years to 'Happy' and is used more frequenly now in the UK because it is the word Queen Elizabeth II prefers to use, as she dislikes the connotation of 'Merry's' intoxication. The Queen wishes her British subjects a “Happy Christmas” in her annual Christmas broadcast.
To certain ears “Happy Christmas” conveys a sober, well-earned enjoyment, the satisfaction resulting from hard work and virtuous living. Americans, however chose to keep the original word of 'Merry'.