Did you disable cookies in Firefox settings (Options => Privacy) or use any cookie blocking add-on? Alternatively you might browse in safe-browsing mode.
If yes, then this message seems not to be harmful. Web pages are used to save cookies in your browser in order to persistently save authentication. So when you close your main browser windows and re-open a new browser instance you would not have to log in again. In case you disabled cookies your browser will also not allow to destroy such authentication cookies on purpose. But this can be silently ignored as there is nothing to be deleted.
You can check all cookies stored by your browser in the Options => Privacy screen in Firefox. It also allows you to delete specific cookies.
You can also try the following:
- Log in to Hotmail
- Just close your browser
- Re-open your browser and go to the Hotmail page
If cookies are enabled you're likely to be still logged in. If cookies are disabled you're likely just facing the login screen again.
So if you don't have cookies this might reduce the usability slightly and enforce you to log in more frequently. Remember that other pages might store different things in your cookies (like shopping cart contents or similar stuff). I usually do not recommend to switch off cookies in general nowadays.