Nope, Newton was born during the global transition from the Julian to Gregorian Calendar.
Different countries converted to the new Calendar at different point over a 150-year period
Newton's Birthday was Officially the 25th of December 1642 by the Julian Calendar in use at the time and for almost 70 years thereafter until 1752.
Therefore, during Newton's lifetime (1642-1727), the calendar had NOT switched in England to the Gregorian, making his date of birth only RETROSPECTIVELY 4th January 1643 according to the Gregorian Calendar.
Newton himself therefore always used and celebrated Xmas day as his birthday, and if asked his DOB would always say the 25th of December.

@LenHazell53 Thank you that's wonderful, you are well informed.