Yes and no. The festival of Christmas, of course, is a
commemoration of the birth of Christ - hence 'Christ-mas' - which
mean's 'Christ's birth'. So Christmas has everything to do with
Christ - in that way.
However, no one knows the actual date of Christ's birth - it is
just that we adopt December 25th to celebrate it. This date was
chosen as it was close to the Roman new year festival of
Saturnalia, and so when Emperor Constantine became a Christian in
the 4th century, Christmas was adopted in the place of saturnalia.
So in another way the actual date of Christmas has really nothing
to do with Christ as no one knows the actual date of his birth.
The original idea of Christmas and many of the customs are based
around the birth of christ (If you believe in christ)