In some cases, security add-ons (such as NoScript) or security software suites will affect the way Firefox handles cookies. You may want to check the "privacy" settings in your security software to see whether it might be blocking cookies.

You need to enable third-party cookies if you want to logout from Hotmail. If you do not want to enable third-party cookies (I don't) then you need to remove the live.login and passport.net cookies yourself.

See also Third-party cookies and Firefox tracking protection