Some do, some use December 25th.
I think that 5 or 10 years ago most FR Christians would have been happy to support more Orthodox getting on the same page as most of Christianity and recognizing December 25th.
In the early fourth century, the church fixed the date as 25 December, the date of the winter solstice in the Roman Empire. It is nine months after Annunciation on 25 March, also the Roman date of the spring equinox. The Catholics adopted this immediately and it spread into Protestant faiths.
Orthodox uses a date from the Julian calendar from 46 AD.
Their brand is more uncorrupted by the Roman Empire.
And no, nobody here a decade ago gave a moment’s though to getting the Orthodox Christians to coordinate with western churches. (Except the Pope of course)