A number of users are experiencing issues when using iCloud Mail. Some customers are unable to log into their mail account using the Mail app or third-party apps.
As Apple now officially confirmed iCloud Mail appears to have been affected by an outage since 3:09 p.m. CET. The notification states:
Today, 3:09 PM - ongoing - Some users are affected. Users may not be able to access iCloud Mail.
The nature of the problem was not explicitly stated. Apple only states that some users cannot access their iCloud Mail. The problem also appears to be limited to iCloud Mail.

iCloud Mail – It's not a bug, its a feature
That said, all other iCloud services seem to be running normally so far. Interestingly, not all users are affected by the restriction, as various reports indicate. Twitter posts show that a number of users are complaining about not being able to access iCloud Mail, while other users have limited access. However, some are able to use the service without any problems. Outages of online services are common and have also occurred several times with Apple's iCloud products. There was a similar outage with iCloud Mail in April this year. Be that as it may, we will update the post as soon as Apple has fixed the problem. (Photo by hadrian / Bigstockphoto)
Update:
Apple now seems to have fixed the problem with the mail service. The confirmation comes from Apple's system status website.