My Z710A with the 23 HP Kohler didn't come with a oil cooler. Some of those Z700, Z800, and Z900 series Ztraks came with oil coolers.
So, this is a winter project for now, as I have decided to install a John Deere/Kohler oil cooler on my engine. Here is a picture of the oil cooler less the sandwich adapter. I have bought a different adapter for the cooler. I will not be connecting it to the top engine housing as the factory ones. Instead, I will form a bracket to install it some three inches on the right side of the engine bay with a 4' x 4" 12 volt fan to push the air into the cooler fins.
Now, the big 64 thousand dollar question. How much engine oil should I add to the crankcase? It appears to me the oil cooler probably will hold about 1/2 pint or less. With this extra oil in the crankcase and it will show more on the dipstick. The user manual doesn't state anything about this on engines that have the factory oil cooler installed.