C is not a registered protocol
You can double click on a .EML file in Windows Explorer and have it displayed in Thunderbird if the entry for .EML in Tools -> Folder Options -> File Types is set to use Thunderbird. If you configure Thunderbird to be the default email client it should do that. However, it may also display a "c is not a registered protocol" error message. The "c" in this message is the drive letter, so if you have other partitions you might see other letters.
This bug has not yet been fixed (as of December 2006—see comment #24).