All About Electrolytes
Since there seemed to be some confusion on how electrolytes work in your horse's body, I thought I'd do a post just on that! Horses (and humans!) function on 4 primary basic electrolytes: Sodium (Na), Potassium (K), Chloride (Cl) and Magnesium (Mg). Together, you may notice that these things form several salts, including common table salt - NaCl. In the body, electrolytes pull water out of the digestive tract into the gut, causing the horse to feel thirsty and subsequently drink more water.
Horses DO have different concentrations of these electrolytes in the body than people. HOWEVER, the body is also very capable of regulating these relative concentrations, especially when the horse is on a balanced feed. If you wanted, you could dress your horse's feed with common table salt as an electrolyte boost with no ill effects. Electrolytes like potassium help the muscles function well, but most horses don't need a boost in any electrolytes specifically unless they are having a serious medical issue, at which point you should seek a vet's advice.
The moral of the story: adding a small amount of salt into your horse's diet should help them to drink more and to fend off hydration. Gatorade will not hurt your horse in reasonable quantities, because the body is capable of regulating its concentrations of salts. The most important thing when giving electrolytes is to monitor their water intake so that the electrolytes cannot exacerbate dehydration should they refuse to drink. I hope this helps everyone!