You can open MuseScore mscz files with the MuseScore Songbook app. Upon opening the mscz file will be added to the apps internal library.
You can use apps such as Mail, Safari, Dropbox and more to browse for mscz files and open them directly into the MuseScore Player app.
Use third party file manager apps such as ASTRO File Manager or ES File Explorer to browse for mscz files on your local storage. Also Dropbox, Google Drive, Gmail, Mail and the Browser will open mscz files directly in the app.