Q. See question above. Does the greeting to Gentiles that you mentioned is permitted to have then in mind that you are addressing and saluting Hashem, apply also to the season's greetings like New Year and Happy Holidays?
A. Horav Dovid Pam, Horav Aharon Miller, Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit'a maintain that it does not apply yo New Year and other season's greetings, as it seems obvious.
However, a posuk in Tehilim (87: 6) mentions that "Hashem Yispor Biksov Amim or He counts in the script of the nations."
One of the interpretations of that verse was given by the Magid of Mezeritch zt'l, that to the great wonder of his many disciples would bless them during the Gentile's New Year with a brocho of Leshono Tovo or have a Good Year. He would explain to his very surprised spiritual elevated Talmidim, that during our day of Judgment Rosh Hashana, our Nation is accused by the Celestial Court of only repenting and doing Teshuva out of fear of what the future may bring and not for the true love to Hashem.
What does Hashem do then, he withholds the very final judgment and giving of the sentence until the Gentile's New Year. Then with the company of the Celestial Court He visits the places where many Gentiles celebrate their New Year, and to the dismay of the court, they observe the drinking, drug use and the often real depravity partying and even orgies involved. Then Hashem tells the court, you see now the difference? Let's now pass judgment on the Jewish Nation and bless them with a true Shana Tova a "Good Year."
The Magid explained that is why Hashem counts to the Year of the Nations and then decides to bless us with a "Good Year" as he is also doing.
In that sense, the words of the Igro D'Pirko and Chida mentioned, would also apply to our common New Year greetings.