How do I respond to someone wishing me a merry christmas?
"Auguri per un felice Natale a te e famiglia!"Edit: I now realize I didn't explain this very clearly - the Italian sentence I wrote is what I want to respond to.

Question

How do I respond to someone wishing me a merry christmas?
"Auguri per un felice Natale a te e famiglia!"Edit: I now realize I didn't explain this very clearly - the Italian sentence I wrote is what I want to respond to.

Answer

Sorry, this was supposed to be an answer, I realized later.
So it should start with 'anche' or 'anche' should be present:
- Buon Natale anche a te e {ai tuoi cari, alla tua famiglia}
(I would not drop /tua/ in /tua famiglia/)

Answer

Hi Anna
There is no a particular way of saying but as Andrew said , you can replay:
Tanti auguri or Buon natale anche a te.
There are two others motto very nice:
1 - Buone fatte feste = a wish after Christmas
2 - Buona fine e Buon principio = a wish to indicate a wonderful end of year and stunning new year.

Answer

You hit quite near the center.
1a. Auguri di un felice Natale a te e alla tua famiglia!"
1b. Auguri di un felice Natale a te e ai tuoi cari!
OR 
2a.  Auguri di Buon Natale a te ...

Note that in forms (2), which are more common, the article is not needed.
By the way: Buon natale e Felice anno Nuovo a te e ai tuoi cari.