Creating a new iCloud account just simply creates a new email account and Apple ID. The original account you maintain and remains active. Apple cannot and will not delete iCloud accounts.
So really, you will have two email accounts -- the old and the new.
Don't change anything with your existing MobileMe account. The only change really is when you moved from MobileMe to iCloud, which what most people did -- and got us all in this mess.
So to get a new iCloud account got to Settings (on the iPhone or iPad) -- Mail, Contacts, Calendar -- Add Account -- iCloud -- Get a Free Apple ID (at the bottom of the screen) -- which will take you to New Account screen.
Again, once you have established this new account, go delete the old account from your iDevice. You can delete the data off your iPhone (as long as you have the data backed up on iCloud or iTunes -- I prefer iCloud because I get everything back right away once I re-added the old account back to my iDevices). Or you may keep it on there; you may just end up with duplicates.
Once the old mail account is deleted, go to Settings -- iCloud and log with your new iCloud/Apple ID.
Go back to Mail, Contacts, Calendars and log on with your new iCloud/Apple ID account. Don't worry about if this new account works or not (mine had a problem connecting to the server, so it kept failing retrieving the Welcome email from Apple).
Restart the iDevice (Home button and Power button), then go back to Mail, Contacts, Calendar to add the old account back.
If you have a laptop or a desktop, try sending yourself email to both new and old email accounts, to test. It may not work immediately, as it took some time for my iPad 2 to get pushed emails, but an hour or less later, it started working for it. I think my 4S took some time, too.
Once you get that pushed email, you may go ahead and delete the new account off the Mail, Contacts, Calendar.
Don't forget to log on to iCloud with the original account after you delete the new account off the mail settings.
Again, don't worry, your original email address will stay intact. This really worked for me and I only have my original MobileMe account on my iDevices -- the new account has been deleted off my devices.