TerryNet, thanks for replying. No, I'm aware of the difference between the accounts. I haven't checked the box for saving the password, in the Live Mail application, which means I have to enter the password to send and receive new emails. But the folders are still visible, without entering the email account password. This is what I find strange.
But maybe it's because I mistake the email client as more similar to a web browser, I mean having the web browser doesn't mean all the mails are visible -- unless you know the password to the email account. But, then, in the mail *application* the folders and mails are visible even before entering the account password. But, like I say, I suppose it's just that I don't understand what the mail application is supposed to be. I still think my view makes some sense, though.

That the mails should be all visible (even those that aren't really stored on the harddrive, but are actually only in the Hotmail/Live Mail online account). I suppose there's no 'solution' to what I would prefer, since the app just isn't what I assumed.