I have no problem accessing and using iCloud webmail. When I use the same user name (my iCloud email address) and password to link up with Mail (Apple Mail, that is) the same password is rejected. I thought that the same user name and password was accepted for all iCloud functions but apparently not. How do I set a password for Mail?
MacBook Pro, Mac OS X (10.7.2)
I have the same (or similar) issue; Mail cannot connect to iCloud Mail because of rejected password (on Mac, iPad, and iPhone). However, I have noticed that as long as I'm logged in to iCloud in my browser, the password is no longer rejected in Mail (on either device). Hence, a temporary fix for you might be to do what I have done - keep a tab with iCloud open in your browser at all times until Apple has posted a fix for this issue.
eMail Access
