Praise be to Allah.
It is not
permissible for the Muslims to exchange greetings on the occasion of the
Gregorian New Year, and it is not permissible for them to celebrate it, because
both of these matters involve imitation of the kuffaar,
and we have been forbidden to do that.
(blessings and peace of Allah be upon him) said: “Whoever imitates a people is
one of them.” Narrated by Abu Dawood, 4031; classed
as saheeh by al-Albaani in Saheeh Sunan Abi Dawood
offering greetings on this day that comes back each year comes under the
heading of celebrating it and taking it as a festival, which is also forbidden.
And Allah knows best.