This page http://support.apple.com/kb/HT4929 "iCloud: What if my device or computer doesn't meet iCloud system requirements?" had obviously not been read by my support agent, though it is dated 12 October.
It says this: If you created an iCloud account from an iOS 5 device or Mac running OS X Lion, but have other devices or computers that don't meet the system requirements, you may be able to use some features of iCloud with limited functionality. Please note that devices which do not meet the system requirements for iCloud are not supported by Apple or AppleCare for use with iCloud.
(my bold text)
In other words, as an Apple support agent he is not allowed to give me any advice relating to a Mac running Snow Leopard, which was certainly the impression I got.
It then goes on to say: If you want to check your iCloud Mail [Calendars/Contacts], you can do so by visiting icloud.com from a Mac or PC (as long as it meets the browser requirements for icloud.com).
The browser requirements took a little finding but they include Safari 5 and the latest versions of Firefox and Google Chrome, as well as IE8. There is no word about whether iOS 4 Safari will work - can someone who has set up iCloud and who has an iPod Touch, iPhone or iPad running iOS4 try accessing their iCloud account and looking at calendars, contacts and mail? [re-reading your original post, Gigi1701, I think you say you can't do this but please confirm]
For Mail, it also says: Alternatively, you can configure a mail application that supports IMAP via SSL for use with iCloud Mail. More information is available here http://support.apple.com/kb/HT4864.
That page gives precise server information which would allow you to set up Mail.app in Snow Leopard and Mail on iOS 4 devices to work with iCloud mail. It seems acceptable to be able to access the iCloud calendar via the iCloud website but not so handy for contacts as they would then not be automatically synced to Address Book on the Mac or contacts on your mobile device.
There is information out there about how to access iCloud server settings: one page gives the following settings:
Calendar p03-caldav.icloud.com, Contacts p03-contacts.icloud.com
These may be experimental or temporary settings used for the beta testing phase and I have also seen p04 and p06 prefixes.
Maybe significant: HT4929 above gives the incoming and smtp server addresses as imap.mail.me.com and smtp.mail.me.com while the page with the p03 settings prefixes these with p03- in each case. I hazard an educated guess that you could set up the iCloud calendar as a CalDAV account on your iDevice by entering caldav.icloud.com as the server address. I also suspect that you can do the same with the iCloud contacts by entering contacts.icloud.com as the CardDAV server address. The other information you need to put in is the username (I've seen somewhere that you don't include '@ me.com') and password. Gigi1701, how about trying that and reporting back? Then you wouldn't have to carry your iPad all the time in case you need to add a new contact.