It makes sense to humans that a big, ice cold drink would be the best way to cool a horse down- but a horse's body is designed to drink from warmed water sources when hot and thirsty and cold water can actually make a horse sick! Instead of cold water to cool a horse down, provide tepid or lukewarm water. Cold water for a hot horse can shock their system and make them very ill. A hot horse that has just been worked hard should be offered room temperature water, a few gulps at a time, until the horse is cool and breathing normally.
It's not a good idea to hose a horse with cold water to cool a horse down, either. Cold water sprayed on the large hot muscles of a horse can cause a painful, dangerous ailment called Tying Up. It's best to spray a horse down with tepid or slightly warm water rather than cold water. If cold water is the only option to use for hosing off your horse, spray the legs directly with cold water for 5-10 minutes. On the legs of a horse, the blood vessels run just under the skin. By spraying the legs with cold water, the blood cools and circulates through the body, cooling as it goes. After several minutes the larger muscles groups will be safely cooled by the circulating blood and it will be safe to spray the entire horse's body with cold water.
As you can see, cold water to cool a horse down just isn't the safest way. Cold water is acceptable for horses resting and not overheated, but never as a method to cool an overheated horse.