Good question. It'll save in whichever file type your default email client creates. For example, my default email program saves it as a .eml file. Thunderbird and Outlook may be different.
As to what to do with a .eml file would be another story. I don't know if my default email program would allow me to import it or not...but I'm not going to test it. I had a horrible experience with this a few computers ago with the end result being absolutely unable to delete an "unrecognizable file" from my desktop. It was 0 bytes with a 255-character filenames consisting of gibberish.
I think attachments are the OP's problem, so download 'em to a backup plan.