Wishing a ‘Merry Christmas’ was first recorded in 1534 when John Fisher (a Bishop) wrote it in a Christmas letter to Thomas Cromwell saying “And this our Lord God send you a merry Christmas, and a comfortable, to your heart’s desire.”

There’s also a carol “God Rest You Merry, Gentlemen” which dates back to the 16th century in England.
In the English language of the time, the phrase ‘Rest You Merry’ meant “[May] God keep you and continue to make you successful and prosperous, Gentlemen”
The term ‘Merry Christmas’ might have also been made very popular in 1843 by Sir Henry Cole who sent a Christmas card with “A Merry Christmas and a Happy New Year to You”.