An English admiral used the term Merry Christmas for the first time in an informal letter in 1699. The words Merry Christmas appeared for the second time in 1843 in Charles Dickens', "A Christmas Carol". The term Merry Christmas is not only used by the Christians to greet each other during the festival of Christmas but by all, irrespective of class as well as religion at the time of the Christmas Festival. In the term Merry Christmas, ‘Merry' stands for happiness while ‘Christmas' meant Christ's Mass in old English. Many people use the word happy instead of merry to wish each other during the festival of Christmas. This phrase Happy Christmas gained much popularity in the 19th century. So you can use either greeting. Source: Wikipedia

I believe that this is optional. I am not for sure about this but I do believe that in some part of the United Kingdom ¨Happy Christmas¨ is accepted while in U.S ¨Merry Christmas¨ is most commonly used. If you say Happy Christmas, it is not incorrect. It´s simply not heard very often and may sound peculiar to the ear of native speakers who are accustomed to hearing Merry Xmas.

It's just a custom to say "merry Christmas" instead of "happy Christmas" there is no one reason for it.

"Merry Christmas" is a set phrase that has been held onto from years past and is what most people are familiar with hearing. This is a rather unique phrase today, since "Merry" is not often used in modern language... so it has an old-fashioned feeling. you can say "Happy Christmas" and someone will understand you, but it sounds strange.