This is a known issue with the standalone Opera Mail. To work around it, in the signature editor, make sure HTML mode is selected and just type "test" and ok out etc. Then, close down Opera and edit signatureN.txt (where N is the number for the account as seen in accounts.ini) in the "mail" folder (see Menu -> Help -> about Opera Mail" for the location).

Then, in the file, you just use HTML markup.

<img src="url to image">

You can remove the "test" obviously.

If you don't like doing this, you can use Opera Mail that's built into Opera 12. It doesn't have this bug. In Opera 12, you just have to go to "Alt + P -> Advanced -> Programs" and add/set http and https to "open with default application".