Horses do not vomit, but do they experience motion sickness? Travel sickness in horses actually means something different - a respiratory condition also called shipping fever.
Some vets argue that we have no way of telling if a horse is motion sick. However, there's some evidence that some horses may colic during rough voyages at sea - which could be stress, a change of feed, or seasickness. We aren't entirely sure - and we can't ask them. (Dogs and cats often get "car sick").