One tradition I notice in Japan is that you can never greet people with "Happy New Year" before Jan. 1; and that's why post offices in Japan will keep all your new year greeting cards (nenn-ka-jou) until Jan. 1 and will only deliver new year greeting cards on or after Jan. 1. (I guess China in the older days had such traditions too, but now there have been so much influence from the Western world that nobody remembers this tradition.)
In comparison, in Western countries it is very "loose", you may in Dec. (or even in Nov.) send out new year greeting cards, it seems there are no Western rules requiring new year greetings have to arrive on or after Jan. 1.