Brewer's Dictionary of Phrase and Fable/Sick as a Horse
Sick as a Horse. Nausea unrelieved by vomiting. A horse is unable to vomit, because its diaphragm is not a complete partition in the abdomen, perforated only by the gullet, and against which the stomach can be compressed by the abdominal muscles, as is the case in man. Hence the nausea of a horse is more lasting and more violent. (See Notes and Queries, C.S. xii., August 15th. 1885, p. 134.)