Summary. As of about 1PM Central Time, the Apple iCloudemail server is down and the service not running.
Apple has posted an update on the iCloud status page. Screen shots below show the current user experience.
According to the update (below), the iCloud email service should be restore as soon as possible.
Given the broad awareness of Apple’s recently launched cloud-based services, this outage will likely be reported by mainstream media outlets. This is a surprising outage considering the reliability of Apple products and services.