Try the Mac OS X 10.6.8 Update Combo
Then restart your Mac.
You could also try deleting your Hotmail keychain. Open Keychain Access.
/Applications/Utilities. Select Passwords on the left. Delete the Hotmail keychain.
Quit then relaunch Safari. Navigate to your Hotmail account. Enter your user name and password. You should be prompted to save that data to a new keychain.
You might want to consider accessing your Hotmail account via Mac Mail rather than using web based mail.
The same thing is happening to me and nothing I have tried or that people have suggested in any other forum has worked. I just updated to 10.6.8 and then updated Safari to 5.1 and it's still not good. Alot of people have been complaining about this and also the cookie handling in 5.1 and so far Apple just isn't addressing the issues. Hotmail help according to alot of people is also useless. I'm using Firefox until they get this all fixed, but I have to say, I'm very disappointed in Apple this time around, especially since people have been talking for over a month and they haven't fixed it.