This is why the YouTube compilation video was invented: someone put together a collection of scenes where Foghorn Leghorn paddles the Barnyard Dawg's ass. This gag was in the first Foghorn cartoon ("Walky Talky Hawky") and became a staple of the series.
I've always found the Foghorn/Dog conflict funny because it's different from most cartoon conflicts. Usually it's predator vs. prey, or some variation on the idea. (Foghorn Leghorn, of course, was conceived as a twist on the predator/prey formula, a huge prey stalked and eventually beaten by a tiny predator, Henery Hawk.) But these guys don't want to eat each other, or even kill each other; they just want to cause each other as much humiliation as possible. That's why the paddling gag works so well: there is absolutely no point to it except for Foghorn to amuse himself by beating up the dog. It's part of what made Foghorn Leghorn a pleasingly amoral series at a time when most big cartoon series were coming down on the side of good and right (antagonist loses, protagonist wins).