In the earlier versions of Windows Live Messenger, when you clicked on the Mail icon / button, Internet Explorer would automatically open up and log you into Hotmail, irrespective of your default browser.
However, beginning with Windows Live Messenger 2009, clicking this Mail button opens Hotmail in your default browser. If the browser is not Internet Explorer, it will not provide the automatic log-on into Hotmail.
Hotmail in IE does not require installation. Just download the executable and run it directly.
To set Internet Explorer to open when you click the Mail button in Messenger, choose the Internet Explorer button. Should you wish to set it back, choose Default Web Browser. Once you have made your choice, choose Done and no further changes should be needed.