I'm going to answer this directly rather than post it.  We get into
debates about celebration of CHristmas in late December each year.
I'd like to avoid any more than one of these debates per year.

Some sort of celebration of the Incarnation goes back fairly early.
In Rome, the earliest evidence is from 336 AD, when the feast is
reported as already general Roman practice, as a celebration of
Christ's birth.  In the East, the earliest celebration was Ephiphany,
which involves both Jesus' birth and baptism.  This was celebrated on
Jan 6.  It is widely believed that the Dec 25 date was chosen to
compete with the pagan holiday Natalis Solis Invicti, though of course
there's no real way to know.  (This is just a guess.)  It seems to
have been fairly common for Christians to put celebrations opposite
major pagan celebrations.  This has a number of advantages, including
give your kids something Christian to do when their friends are having
pagan celebrations.  (For an equivalent in modern times, not how the
Jewish Hannukah has been developed into competition with Christmas, I
think largely to give Jewish kids something to do during a Christian
holiday season.  I think it's a reasonable strategy.)  Presumably this
motivation does not apply to the Eastern version, Epiphany.  

The purely Christian part of the holiday is a celebration in church
(the Christ Mass).  However from the beginning there was also
merrymaking of various kinds, whose nature seems to depend upon the
specific culture.  E.g. American Christmas customs seem to go back to
German and English roots, whereas other countries have other customs.
The actual Christmas church services however are much more similar.

Little reliable information is known about St. Nicolas (on which Santa
Claus is based).  There are stories about him helping many people,
particularly children.  (One of the nicest presentations of the
legends is a short oratorio "St. Nicolas" by Benjamin Britten.)  I
think people assume he really was a bishop, though there's essentially
no historical information on him.  He is listed as bishop of Myra in
Lycia.  Sorry, I don't know where Lycia was.  Presumably in the Roman
empire, as he was supposed to have been imprisoned by Diocletian, and
there was a church to him in Constantinople by 565.  Britten's score
claims he was born in Patara in Asia Minor, and died in the first half
of the 4th Cent.  It implies that Lycia is in Asia Minor.  (I don't
know how much of Britten's information is legendary.)  He is
considered (for reasons I don't know of) the patron saint of Russia
and Greece, but of course the USSR, and all of the people currently in
Russia are much later than the period he would have had to live.
The celebration of Christmas is earlier than St. Nicolas, obviously.

The whole business of trying to discredit holidays by claiming that
1000 years ago there were pagan roots seems irrelevant to me.  The
relevant question seems to be whether celebrating the holiday now
helps us appreciate Christ and worship God.  I suspect in the case of
Christmas the answer is "yes and no".  Certainly a good deal of the
commercial surroundings, and the general frentic attitude of the
season, seem far from Christian.  However many of us find the midnight
service celebrating the birth of Christ quite important and moving.  I
personally do my best to ignore much of the rest.  But I find the
scrooge-like attitude of some fundamentalists far from Christian.
What is wrong with having Christian celebrations?