How can I send mp3 files through email?

Attach it like any other file. Have you tried this?
Some ISPs may filter out music files and have limits on attachment sizes.

You can zip the file if your isp or email client doesn't allow this file type to be emailed.

MP3 files are already compressed so another layer of compression is not going to save much space at all. Sending a single file at a time (assuming it's legal for you to share it) should not be an issue with email.

I think he was referring to hiding the extension by zipping it. Many anti-spam/AV enterprise programs look into archives so I'm not sure it would help.

You're right, most spam/AV engines will look inside the archive and even go in more than one level.

What I do to get around that is rename the extension using an underscore.
MySong.mp_