Q. As the holiday season approaches is there a problem with mailing a season greetings card?
A. The Talmud (Gittin 62a) teaches that in the interest of peace, greeting an idolater is permitted even during their feast days as long as you don't enter his abode. During their sacred days it dictates; "Should he meet him in the street, he should then greet him in a soft voice and with a downcast head". This is too the opinion of the Shulchan Oruch (Y.D. 148, 9). There are different opinions as to whether the Gentiles of today are considered true worshipers and if their beliefs are idolatry or no.
Horav Shlomo Miller's Shlit"a opinion is that sending non-religious, non-specific, generalized season greeting cards is permitted. It is preferable nonetheless, to send them so that they arrive earlier or after the actual celebration day.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a