Have been testing for some time now.
I use Nokia Messaging.
Do not sett the emailclient to "Update Automaticlly". This is for IMAP and POP and as I see it have nothing to do with Nokia Messaging.
Instead open Nokia Messaging and "Edit Account". There I have set mine to sync everyday between 06:00-23:00 and "Send and Recive" As Soon As Possible. I have also unchecked Sync Sent Items and Sync Drafts.
Now Nokia Messaging seems to get Pushes from the Nokia Messaging system and then the client sync not otherwise. But Sometimes some emails never get synced, so always check your hotmail on the web from time to time. And its not instantly syncing. So dont trust it 100%.