Saying "Happy New Year" on the Christian New Year

Q: Is it permissible to say "Happy New Year" on the Christian New Year?
A: No, because the Christian year is connected to idol worship. It is forbidden to give respect to idol worship in any form. A person who says "Happy New Year" is not worshipping idols but he is acknowledging it in a positive way. It is similar to the Halachah that it is forbidden for a person to say to his friend: "Let's meet by this church," since he is acknowledging idol worship. One should therefore say: "Good morning," "Good day" or something else.