You have to remember that when you access a particular domain all cookies from that domain will be stored in one place.
So if you access hotmail.com and login. The login information ( if you click on Remember me) will store the info to your browser's cookie.
Any other access to hotmail.com will always use the same cookie file which means all info is stored on the same cookie. The system all that it does is use these cookies to remember you.
Maybe you should either
a. use no cookies for that site.
b. look at your prefs in your hotmail account.
c. Use different browsers to view different sites
d. Delete your cookies for M$N.