Rats and horses can't vomit.
Horses have an extremely strong valve between the esophagus and the stomach; overpowering that valve in order to send food out of the stomach is nearly impossible (this is why colic is such a serious problem for horses). Rats have a powerful seal separating the esophagus from the stomach that they are unable to open. Their digestive systems are a one-way street, which means that when they overeat they simply have to feel miserable - or, in extreme cases, die.