If you're willing to carry around an extra device, you might find it easier just to carry around an extra battery for your phone. However, as other's have noted, music playback is a relatively low drain on your battery. The biggest consumers of power on a phone are typically the screen and networking (cell or wifi).
An mp3 player would be loaded with music by connecting to a PC. You won't have to worry about losing your music, as long as your mp3's on your computer are safe and backed up.
There are a lot of ways to get mp3s legally these days. You can buy mp3s on amazon, itunes, etc. Streaming services (spotify, pandora, etc.) are also an option, but those will require network usage and hence drain the battery faster. Also, if you already have an extensive CD collection, you can rip those to mp3s via Windows media player or iTunes.