When you use free email services like Hotmail, Gmail, etc. They want you to access your inbox through their site to cram you with ads. They have no POP/IMAP servers you can connect to with Thunderbird/Outlook/etc. Now with Thunderbird and WebMail, you can! (I sound like an ad XD )
WebMail Addons:
http://webmail.mozdev.org/
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Sadly, you cannot SEND emails using this. Sorry for not including that.