The question took me back to one of the first questions I was asked in California, that being, “Do horses get seasick?” That one’s a pretty good story – I’ll have to write about it.
Anyway, motion sickness in humans is a pretty complex process; the brain actually senses motion through three different pathways of the nervous system, including the eyes. Since the body isn’t doing to work of moving, it’s thought that the input to the brain is uncoordinated (for example, the eyes say you’re moving, but the inner ear says you’re not), which somehow leads to motion sickness. Even so, this is just a hypothesis; if the conflict theory were really it, how do you explain why blind people can get motion sickness?
But back to horses. Even if horses did get motion sickness, there’d likely be no way to tell. After all, horses can’t throw up, so one wonders what signs might indicate that a horse did have motion sickness.
Bottom line: nobody really knows (and I don’t know how you’d tell)!