I didn't find any solution for this on the internet, so I came up with my own and thought I'd share in case anyone's having the same issue.
Nautilus in Ubuntu 12.10 doesn't allow you to create your own custom execution script (unlike earlier versions). The workaround is normally to create a desktop entry in /usr/share/applications/ called processing.desktop with contents something like the following:
The Exec line basically says launch processing (customize the path to suit your installation) and the %F passes it the file path. However, nautilus doesn't execute this in the way that you'd expect it to work from the command line. Something to do with strings .... You end up launching an empty sketch. So instead, we'll create a little bash script called launchprocessingfile that DOES work as we'd expect, and point our processing.desktop file there instead:
Place the file in a folder included in your $PATH variable:
$ sudo mv launchprocessingfile /usr/local/sbin/
If you want to check to make sure the folder IS in $PATH,
$ echo $PATH
Optionally, you can download a 48x48 pixel Processing icon, name it processing.png, and place it in /usr/share/pixmaps/ (matches line that says Icon=processing in the processing.desktop file above).
In Nautilus, right-click any pde file. Choose Properties. Click on the "Open With" tab, then "Show Other Applications" and select Processing from the list. Click "Set as Default", then close. pde files should now open with Processing by default!