Question: Is it permissible for a person to initiate the well-wishing for
the new year to someone?
Response: If someone wished you well, then return the greeting to him, but
don't you be the one to initiate the well wishing to anyone – this is the
correct position in this matter.
If for example someone said to you 'we wish you well for this new year', you
should say "may Allaah greet you with good and may He make it a year [filled
with] good and blessings", however, don't you initiate [the well-wishing] to
the people. [This is] because I do not know anything from the Salaf that
they used to greet [the people] with well-wishes for the new year. Rather,
know that the Salaf did not adopt Muharram as the beginning of the new year
until the caliphate of 'Umar ibn al-Khattaab (radhi-yAllaahu 'anhu).
Shaykh Ibn 'Uthaymeen
I'laam al-Mu'aasireen bi-Fataawa Ibn 'Uthaymeen - Page 372