It's really easy on a jailbroken device, but it can also be done on a stock iPhone. I just tested it and it worked fine. If you download the music with the Downloads - Download and Download Manager app, that will be the only app you need. Otherwise, you'll also need DropBox. Move the music into one of your DropBox folders and then link DropBox to the Downloads Manager app. Now transfer the song to the Downloads Manager app and then select email. If a song is not already in your DropBox folder and you aren't at home, you could login to your computer remotely with a VNC app, transfer the song to DropBox, and then follow the above steps. But if you're going to do that, you might as well just email it from your computer (remotely).
If the song is in your DropBox folder or if it was downloaded with the Downloads app, it's pretty simple. This is a screenshot of the Downloads Manager app: