“Deck the Halls” is a song in the public domain. So is Handel’s “Messiah” … the whole thing, including the ever-popular “Hallelujah” Chorus. Lots of popular Christmas songs are in the public domain (but lots are not).
Does that mean that you’re free to use these works wherever and whenever you want?
The works themselves are in the public domain; that means that a musician or chorus can perform them, arrange them, make a derivative work from them, do whatever creative thing they want to do with them … but that performance, arrangement, derivative work or other creative thing based on the song is absolutely protected by copyright. That means that, unless you own that copyright or have licensed rights under that copyright, you are NOT free to use that performance of the public-domain work. Your unlicensed use of the work would be considered copyright infringement.
Have you bought the recording? Great! You then bought the license to play the recording privately in your home or car … in private.
Suppose you’re having a party … can you still play the recording? That gets a bit more tenuous. The practical answer is likely that no one will enforce your technical infringement of the copyright license you purchased when you bought the CD, but technically you are infringing on the copyright.
Suppose you own a business and you play the audio in your business? There you’re going to run into trouble. The copyright police are ever-present, and they come into your place of business looking, feeling, smelling and acting just like normal customers … until you get the cease-and-desist letter from the copyright holder citing the date, time, place and song being played without license. It happens to big business (that’s why MUZAK® exists) … and it happens to mom-and-pop shops, even when the mom-and-pop shop is just playing the radio or a CD that Mom or Pop purchased. That’s public performance, and public performance is NOT licensed by the purchase of a copyright-protected audio recording of a performance, even of a song that is in the public domain.