There are two means of cooling with water. The first is evaporation, which works with any water on the skin. Efficiency depends on the humidity. Sweat is the body providing this mechanism by itself.
The second is the heat capacity of water, which is 4 times greater than air. So if the air next to the skin is 10 deg cooler than the skin, it will take X amount of energy to warm it - thus transferring X heat. But if the water next to the skin is 10 deg cooler, it will take 4X energy to warm it.
Of course, if the water is cooler than the air, it will absorb even more energy while heating up. Water moving over the skin would be optimum, since the heat would continuously transfer.
If you have limited amounts of water, then sponging it on, letting it absorb heat, then scraping it off and replacing it is the best you can do. If you have a hose or lake, then let it flow. Either is better than waiting for air to do the job. After all, the insulation provided by hair to keep the horse warm also acts to retain the heat after exercise.
None of that is very surprising. The argument made prior to the Atlanta studies were twofold:
1 - The veins contract when cooled, so cool water will actually REDUCE heat transfer. In fact, the shrinking of capillaries isn't a big factor, while the cooling effect of water is. I can remember when the common wisdom of joggers was that you should shower off with warm water to prevent the blood vessels from shrinking. It is not true with humans, either!
2 - Muscles will be shocked and contract when suddenly cooled, creating muscle spasms. Doesn't happen that way.
"Statement #2 above has been the source of some controversy over the years because of the belief among certain horse trainers that ice cold water placed on a hot horse's body will "shock" the horse's thermoregulatory system into shutting down blood flow to the skin. This belief has been found to be wrong. Extensive research conducted during 1995 at the University of Illinois and University of Guelph and at the 1996 Olympic Summer Games in Atlanta proved conclusively that horses working under hot and humid conditions were better able to maintain core body temperature within an acceptable range or even reduce it during rest periods after intense phases when ice water baths were used. Liberal application of icy cold water to overheated horses helps to dissipate heat not only by providing more water to evaporate from the skin, but also by direct conduction of the horse's body heat into the water which runs off the horse, carrying away excess heat in the process. According to University of Illinois researcher Dr. Jonathan Foreman, "In our treadmill simulations of C Halt (a rest period during a phase of the equestrian competitions at the Olympic games), cold water baths were used with significant decreases in core temperatures and heart rates. No adverse clinical effects were apparent during the remainder of Phase C trotting or after exercise. Horses actually trotted more freely after bathing stops."
Managing Heat Stress in Horses - Horses