Speaking from experience, I have always brought my own small cooler with me to the WA to every course. I usually have at least 2-3 bottles of Gatorade and water so I can hydrate in the 90+ temps throughout the day. I have never tried to hide it and have even asked at the course if it was ok and have never been told I could not have it. I suspect that if there is any issue it is more around bringing alcohol to the course and that is what they don’t want. Can you imagine the trouble they could face if someone had a medical emergency from heat exhaustion or stroke because they did not have fluids?