Answer:
Some people suspect so but it hasn't been proven. Most likely the reason they suspect so is because on a breeding farm where many of the horses are related, all the horses are often trimmed and/or shod by the same farrier, and what actually causes navicular is improper trimming and shoeing. It has been proven that all horses with navicular have long, underslung heels and bars that contact the ground or shoe. Constant hammering on these bars through daily excercise injures the navicular and structures around it, resulting in navicular syndrome. So, when on a breeding farm where all horses are trimmed by the same farrier, the farrier they use may allow underslung heels and long bars, thus causing navicular seem hereditary while it is actually the work of the farrier, not genes.