Hello hooey,
Welcome to eQ! You cannot do what you want to do with saving an email to favorites for three reasons. You're on a shared computer in the library you would want people able to see your mail would you? Second it's likely that favorites are cleared on each computer between users and lastly with the way the new Hotmail works each email doesn't have it's own web address, so likely the favorite would only take you to a Hotmail error page.
Sorry we couldn't help you with that however you can always print out the email or make a folder in Hotmail and move the email to that folder so that you will have it for future reference.
Cheers,
Dan