You can create a CONTACT in ADUC, give your hotmail address as the SMTP address and make it primary.
Then open properties of your own account, go to Exchange General tab and click on Delivery Options. In the middle section which called Forward address click Forward To and choose the CONTACT from Modify. Tick the box underneath saying "Deliver messages to both......."
No need to use Outlook and/or OWA for doing this.
