The notion that a hot, recently exercised horse needs to cool down before drinking water is indeed a myth---unfortunately, one of many about horses and colic. Absolutely, it is best to rehydrate sweaty, hardworking horses without delay, but the key is to know how much water to allow at one time.
A horse's stomach is relatively small compared to the size of his body, and it holds about eight to 12 liters (two to three gallons). Once full, the stomach needs to empty before taking in any further water. When a horse is worked hard, his stomach and intestines temporarily shut down while blood flow is shifted to the heart and lungs. Anyone who runs long distances can tell you that they have difficulty keeping down food and water immediately after running, and they are likely to vomit if they have a full stomach as they exercise.
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The same is likely to be true in horses. Therefore, instead of allowing a horse to drink his fill after working, it's better to offer small amounts every 20 minutes. By small amounts, I mean one to two liters (up to half a gallon), and wait until the water has a chance to move out of the stomach to offer more.
It's also important to be aware of how much a working horse sweats to determine how much water he will need to recover. Because of their body mass and the dangerous temperatures that could be reached during hard work, it's critical that horses release built-up heat as they exercise. Fortunately, they are highly efficient at cooling themselves with sweat. A horse can lose
up to 10 percent of his body weight through sweating if worked all day and not given water. That equals approximately 48 liters (about 12 gallons) of water plus electrolytes.
This is why, as you pointed out, it is crucial to provide water at every available opportunity. The water can be given with an electrolyte supplement made for horses, and it can be either warm or cool, although warmer water may be less of a shock to the system.
As an interesting side note, there are horses who live and work in desert conditions in North Africa and elsewhere. These horses have adapted to a hot climate where water is available only infrequently. They store water in their large colons, and as they exercise the colon gradually dries out. When water is available, they take in the equivalent of two to three buckets (about six gallons) at one time without ever showing signs of colic. However, because we have control of our working horses' consumption, a slower reintroduction of water is good common sense, while it makes no sense to hold them off it.
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) лошадь, напоили ее большой порцией ледяной воды, случились колики, которые прошляпили. От всего этого может развиться ламинит как последствия коликов. 
