Do horses get cleft palate?

Yes, although it's very rare.

In some cases it is treated surgically, but some foals are not good candidates for surgery. In some cases, the animal is euthanized. As horses do not normally have a connection between the windpipe and the esophagus, a horse with cleft palate is much more likely to get aspiration pneumonia.

However, some animals with mild cleft palate go on to lead perfectly normal and useful lives.