Is there a Mountain Lion dashboard widget that displays notes from iCloud?
With the caveat that this is just one example of a notes widget, I've used Junecloud's Notefile app a bit, and it seems to fit your requirements of a widget that connects to iCloud. I can sync to iCloud or the app provider's JuneCloud sync. However, Notefile is not a free app (currently $4.99), so you'll need to look elsewhere if you want a freeware solution.

Junecloud also provides an iOS application for mobile devices (iPad/iPhone/iPod Touch) for $2.99 at the time of this answer.