Someone asked me about the Halachic parameters regarding saying the phrase Merry Christmas to non Jews, so here you go:
It would seem that if the current understanding of the phrase is connected with an Idolatrous term than we would not be allowed to wish it on others.
The Rambam writes:
“One may inquire about their well-being – even on their festivals – for the sake of peace.” (Hil AZ 10:5)
(Note: Jews should not wish other Jews Merry Christmas)
When one wishes his fellow non Jew a Merry Christmas they are stating that the person should enjoy their day (ie Christmas).
And this is reiterated in Shulchan Aruch (Yoreh Deah, 148,9) and even by Chazal. (Gittin 61a)
(The Halacha does not state that this would not be allowed if colloquially the phrase included the deities name, for example the Jews referred to Ceasar by name when he himself was worshiped as deity etc.
Also virtually all scholars agree that the name of Jesus is mentioned many places in the Talmud (before removed by the censors).
Another notion is if Christmas is still mostly connected with idolatry or not.
Many fail to understand that Christmas is a National (US) Holiday, and when one wishes their neighbor a Merry Christmas they are akknowleding that this was in the beliefs that this great country of our was founded upon not that they are in anyway assuming the the hearer has sanctified the greeting by linking it to what we would consider Idol worship.
Christ is also a Jewish Term (Used even by Greek speaking Jews in ancient times) that means messiah.
Rav Scheinberg zt”l, also stated that today Christmas is celebrated by most people as a secular holiday, and the name itself does not carry a religious connotation (Divrei Sofrim).
Which is why In virtually every public venue Christmas is far more associated with Santa Claus than with Jesus.
Based on this, Jewish people should have no problem using the greeting Merry Christmas.
(this is clearly just one opinion and there is certainly room for someone who rules another way to hold)