Is there a page somewhere within the episerver mail where visitors can subscribe to a mailinglist?
No, because the default recipient source does not support adding individual recipients - it's import-export lists only. There is however a code sample with its own database tables and stored procedures which I think support it. I can't find an updated version of the code samples, but here's the one for Mail 4.4 which you should be able to use with very small modifications http://world.episerver.com/Download/Items/EPiServer-Mail/EPiServer-Mail-4401/EPiServer-Mail-44-SP1-Code-Sample/
Thanks Magnus (again)