In Japan, we can see cards and signs that say "A Happy New Year" written in English. I don't know why so many people use the word "A" before the words "Happy New Year," but I think this might be a good subject to bring up with my students at this time of year.
In English, I would write something like "Happy New Year!" Most of my English students and Japanese friends, however, tend to write "A Happy New Year!"
Interestingly, most of you would never say, "A Happy Birthday!" or "A Merry Christmas!" as the greeting in your email or card. Well, just apply the same logic to a New Year's greeting, too!
A: "It was nice to see you again. Well, I have to go. Have a merry Christmas and a happy new year!"
B: "Thank you! You, too!"
If you are sending similar greetings in a letter, email, or on a Japanese New Year's card, then you might want to use this format as the initial greeting or closing line (note the capitalization):
Wishing you a very Merry Christmas and a Happy New Year
Have a Happy New Year!
Seasons Greetings!
Happy New Year!
Have a safe and prosperous New Year!
Happy Holidays!
Have a happy and joyous New Year!
One more small bit of advice: in the U.S., only January 1st is a national holiday. The name of that holiday is "New Year's Day." So, if you have to refer to that day in particular, don't forget the apostrophe after the word "year."
With that, I would like to say to all my friends, students, and colleagues "Happy New Year!"
アンミ英会話教室
〒234-0053神奈川県横浜市港南区日野中央2-6-3
パークサイド日野102号室
