Database Mail is an SMTP application, so you need SMTP access to a mail server to send email from it. The free versions of Hotmail and Yahoo! Mail don't offer SMTP access - you access them solely via a web client (which can technically be automated, but not with Database Mail).

If you have either a Hotmail Plus or Yahoo! Mail Plus account you can use these services via SMTP - but those are premium services you pay to subscribe to. You can find the appropriate SMTP server details on their websites.

Regards,

Jacob