Is any music free

ATT does not zero rate those apps.  But many current phones include free FM radio.  If yours does, downloading Next Radio would be possible.   To use you must use the plug in earbuds which act as the antenna.  (No Bluetooth, no line in jack) 

You can use Spotify. It has free plan. But you can't directly download the songs on it. You can use AMusicSoft Spotify Music Converter to do the job and enjoy music offline.

That's not what they were asking. They were asking if there is any music that doesn't count against their data. This is something T-Mobile sometimes offers.

Also, this thread is four years old.

While Spotify offers a free version with ads, not all music on the platform is completely free. Some artists may choose to make their music available for free on platforms like SoundCloud or Bandcamp. Public domain music, created before copyright laws, is also free to use and share.