I just came across this issue and it is truly baffling that Apple doesn't allows access to iCloud.com from a mobile device.
The reason why I wanted to access iCloud from my Galaxy S3 was to test the find My Mac feature and see if it worked. I use the Samsung Dive website to find, track and control my phone should it ever be lost or stolen but for my MacBook Pro I need to use iCloud's find My Mac feature.
But the website doesn't works in Chrome on my S3, giving me a "This browser does not support iCloud.com" message. When I request the desktop site, it loads but it doesn't scales and I can't pinch zoom either. If I try to change the orientation of the screen, the site crashes Chrome. It just can't be used.
It is incredible that Apple has made things this way. There is absolutely no reason why they can't just allow one to access iCloud.com on a mobile device as one would on a desktop computer.