Yup. They don't get them as much as we do - and because they have open roots, cavities on the top of the tooth simply wear down and disappear. Although some people think horses need fillings - nope, there's no sign that they do. Cavities on a horse's teeth tend to be small and they don't seem to have any pain from them.
Horses can get tooth abscesses, however, which can be serious and can result in the need to pull teeth.
Cavities in horses are caused by excessively sweet food - don't feed your horse too much candy - but they aren't nearly as much a problem for them as for us, partly because a horse's teeth are just so much bigger.