So, when you ride a horse into a stream or the ocean, he'll often splash. Is he just having fun?
There's actually two reasons a horse may splash water.
1. Play behavior. I.e., just having fun. One way to identify this is...I once knew a horse who would intentionally splash other horses, and would switch the splashing hoof in order to do so. He wasn't very popular when he insisted on doing this in the middle of winter.
2. Cooling off. Horses know that getting wet cools you down, so on a hot day horses will stop and splash in a body of water. They'll also put their head in water, including a trough or bucket, and shake water over their head. (Horses have pulse points behind the jaw and their ears are also very heat sensitive - if you want to cool a horse off quickly and don't have much water, you splash their ears and their armpits).
A horse that's splashing water on a hot day should be allowed to do so - they're doing it for the sake of lowering their body temperature, and horses are more prone than humans to overheating.