Forwarded email not appearing on iCloud.com

I've been thinking about giving up my Google Apps account now that Microsoft has turned off Google Sync and I can't get push email to my iphone. I hate to lose my private domain email, but I'll eventually get over it.

To test this for awhile and get the feel of iCloud mail, I configured my Gmail account to forward all email to iCloud (but leave a copy in my Gmail inbox). The forwarded email arrives just fine on my iPhone iCloud account (and also my iPad)...but it never shows up on my web-based iCloud.com email. Any ideas? Thanks.

Larry