If it is a cocoa app just type /var/log/system.log or whatever and hit return once or twice.

Another possible way is, if you already have the hidden folder showing in the Finder, dragging and dropping that folder onto the save dialog box.

Drag and Drop is great. It also works from Launchbar, and probably the other launcher apps.
In Launchbar, you can show the hidden files/folders in a directory by holding down the option key when navigating to that directory, ie. if I want to find hidden directories in my music folder, I access my music folder from Launchbar and then hit option-right arrow. The music folder opens with all the hidden files made visible.

Then just drag the file/folder from the bar into your already open Save dialogue and you're done.