You just need to send the appropriate HTTP requests to log in and view your contacts. Then you can parse them out of the returned HTML.
After sending each HTTP request, you will need to process any headers returned - saving cookie values, redirecting when requested etc...
This is all a little fragile. Whenever Hotmail, or whoever, makes changes to their site, your scripts will need to be updated to work on the new layout.
All of the above may constitute a breach of the mail provider's Terms of Service.