iPad iOS 10 - Can I hide songs in the Music app that I have purchased?
Yes, you can 'hide' them.

From the main screen, tap on Downloaded Music.

You'll then be on a screen which is basically exactly the same as the previous one with options for Albums, Artists, etc, which will only show music on your device.

To make it more accessible, I suggest tapping Edit in the main Library screen and dragging the Downloaded Music row up to the top. Note also that whatever you make visible or hidden on this Edit screen will also take effect on the Downloaded Music screen (eg making Compilations visible, Artists invisible, etc).

Note, there is no option to get rid of the initial Library screen. IE we want to effectively make the Downloaded Music screen the top level - there is no way to do that.