I think you can do is press the "zoom" button (+), or I think increasing your form font size will help. (prefs-> documents-> form text field multiline).
Interestingly enough, I just went and signed up another account at Hotmail and received a ERROR Due to an internal error your request cannot be processed. We apologize for the inconvenience. Please try again later.
Sorry, I forgot to mention, if you just switch your user agent to Netscape (Mozilla 4.76), the hotmail compose window works just fine. Which is actually surprising as Hotmail usually finds something to break Opera usage within 24hours of a new release (intentional).
Switch your agent under Prefs->Connections->Browser Identification (use the drop down to switch to moz).
It is doubtful that any MS own properties will ever work good with Opera due to MS's use of proprietary code and (I believe) intentional bug creation.