This isn't windows messaging service. It is either Windows Messenger or MSN Messenger...my guess is that it's Windows Messenger.
In later builds of v4.7, Windows Messenger changed its design: it will now run in the background as a process. There is no UI, no systray icon, etc. You have no idea that it's running. If either IM client was ever set to remember your IM logon password, then Windows Messenger will use it if it somehow got set to run when windows starts.
Launch the main UI, then click Tools->Options->Preferences and uncheck both "Run when Windows starts" and "Allow to run in the background".
However, Windows Messenger would need to have the Hotmail add-on installed in order to send you email alerts. So for this reason, it could possibly be MSN Messenger doing this, but at the very least, you should see a systray icon.