Horses have a band of muscle around the esophagus as it enters the stomach. This band operates in horses much as in humans: as a one-way valve. Food freely passes down the esophagus into the stomach as the valve relaxes but the valve squeezes down the opening and cuts off the passage for food going back up. See: http://funadvice.com/r/14nlfn8lv7n. for more info.
Also their esophagus is connected to the stomach at an angle which shuts once the horse is bloated.