Why do some Jews refer to Christmas as Ex-mas?
Is there anything wrong in Jews saying Christmas?
There are people who don't like saying "Christ", and therefore don't like saying "Christmas." If you don't have a strong secular education, you'd assume that "X" just means "fill-in-the-blank", so "X-mas" sounds like a more "kosher" way to refer to the holiday. (This is what my camp counselors did when I was a kid, and that was their explanation.)
As Ze'ev pointed out, however, "X" actually is just a Greek acronym for "Christ", so you gain little there.
The Vilna Gaon is quoted as saying that "Christ" per se is Greek for "anointed", and does not fall under the Talmud's prohibition on saying the name of a pagan deity. Hence I would assume that the same would apply to the term "Christmas."
(Whether you can wish someone a happy/merry Christmas is a different question...)
The word Christ comes from the Greek Χριστός, and the initial letters, ΧΡ (chi rho), was a common abbreviation in handwritten manuscripts and a symbol for Christianity.
The English Xmas as an abbreviation of Christmas is long-attested: Xres mæsse appears in the "Anglo-Saxon Chronicle" (c.1100). At some point in English the r was dropped from the abbreviation, and the modern Xmas was born. This written abbreviation for Christmas can also be said aloud, pronounced as ex-mas (though it hardly counts as an abbreviation in this case). Collins dictionary gives two pronunciations: