It might feel good in the moment, but dumping water on your body won't cool you off during a race. The most effective way to cool your body during exercise is through the evaporation of sweat, which draws heat away from your skin. When you drench yourself in water, you can actually reduce your body's ability to cool itself through evaporation. So when it comes to performance, drinking water is better than dumping it.
While immersing yourself in cold water post exercise reduces body temperature, dumping water on your body during a race doesn't allow enough time for the cold water to have an effect in cooling your body. So instead of dumping that cup of water on your neck to stay cool, drink it. This will give you all the benefit of hydration, from cooling to performance.