ICloud – What protocol does iOS use to sync Notes to a server

Nevermind, I managed to get it working following the advise of another discussion thread on the Apple forums; namely:

Same thing happend to me on my 3gs, i went to Settings...iCloud...Delete Account then signed in again to add it. The iCloud inbox was displayed afterwards.

This also fixed the problem of notes, which now show up properly on the notes application.

iOS Notes only supports syncing with iCloud or an IMAP email account, according to their Syncing Notes support article.

If your Exchange server allows IMAP access, you could create another account on your iOS device that only syncs the notes for your account. You'll have to ask your Exchange admin whether they have enabled IMAP access and what the settings are for it.

There are a handful of iOS apps which claim to sync Exchange notes, but their reviews indicate that they're unreliable, and it doesn't appear that any of them support Exchange 2010 or 2013. As of this writing, the IMAP workaround appears to be the best option.