Are you attempting to deliver you email via DNS?
Or are you attempting to use your ISP's Mail Server as your "relayhost"?
There should be no reason why you cannot send to a Hotmail account with Postfix, as I do this all the time with my server. And I've used both the above listed methods.
The easiest one to configure and maintain would be the "relayhost", as this essentially will act like an "email client", such as Outlook, Thunderbird or Evolution.
The following article I wrote may help you out:
The following article describes the procedures required for configuring Postfix Mail Server to use a Secure/Encrypted connection for Mail Relay through their ISP/Mail Host Provider.
“root” privileges are required.
Base Postfix Mail Server setup completed
1.Open the main.cf Postfix configuration file for editing.
2.The following information MUST be added, to end of file.
# SASL Authentication
smtp_sasl_auth_enable = yes
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd
*** SAVE CHANGES WHEN COMPLETED ***
3.Create a new file in the /etc/postfix directory called sasl_passwd, and add the following information:
(Creates new file, and opens for editing)
(FORMAT: ISP Mailserver IP/Hostname <tab> Username:Password)
*** Note: Username may be full email addresss ***
*** SAVE CHANGES WHEN COMPLETE ***
4.Run the “postmap” command on the sasl_passwd file to build the database:
*** Creates file called /etc/postfix/sals_passwd.db ***