For new readers to this blog, here is the link to the Happy New Year explanation from a previous post. This is used in the spoken language – in the four days between the end of Christmas (27 Dec) and 31 December. Since Germans have 2 1/2 days of public holidays off for Christmas, people still say ‘Frohe Weihnachten’ on the 26 Dec.
On 01 January, and for several days (or weeks) into the new year, we can greet people with ‘Ein gutes neues Jahr!’
On a greeting card, we use ‘Viele gute Wünsche zum Neuen Jahr!’