Would it be appropriate to translate a Chinese New Year Greeting(s) In Taiwan, on January 1st, for every new year, at Taipei 101 or Kaohsiung Dream Mall they often have singers and other popular actor/actress say new year greetings. 

Why are New year greetings are never translated (both creatively and literally). Here is an example of nba player Jeremy Lin in the New Years commercial using the phrase 猴年賀歲. Is it cultural? or are some things just better left untranslated since it is just a "greeting" and can be expressed with Happy New Years or  Happy Year of the Monkey.

https://www.youtube.com/watch?v=3LEJKHc-f3c
Why translate? It's a Chinese new year. Leaving it untranslated adds the Chinese "taste" of this event.
However, translating this is not inappropriate. It depends on the choice of the event host.