I wasn't searching to find out whether or not changing the thumbnail was possible, I was searching to find out how to go about changing the thumbnail. I guess that's what you get when you make assumptions!
I hope this will be implemented at some point soon. As Gimpster pointed out, a desktop-only option would be fine (similar to changing the added and modified dates).
As it stands now, your notes can really end up with some odd and completely illogical thumbnails!