It makes sense, but it's not something we would say. The set phrase which people say to one another is 'Happy New Year'. Or you might write something like 'Wishing you health and a happiness in the coming year' on a greetings card.
The phrase 'Happy New Year' is used by speakers of both British and American English. The only difference is that the British put the stress on 'Year', while Americans put the stress on 'New'.