The cat wasn't stupid. The cat was fully able to handle his business and escape when it became necessary. That dog, otoh . . .
My Dane used to chase deer regularly in the woods where we walked. At one point, there was an adjoining golf course. It was startling to the golfers and hilarious to me to see a deer burst out of the woods onto and across the green with Bogie, my Dane, close behind!
Bogie would have chased horses, too, in Valley Forge Nat'l. Park, where we would also go, but he was under my voice control and I would simply call him off. The riders were always impressed. Dogs spooking their horses were a constant nemesis to them in parts of the park.
The one and ONLY time I ever saw Bogie intimidated by another animal was when a mother cow bulled him away from her calf.
Hell hath no fury . . .