I think it is fairly well documented that certain breeds (short fat hairy ones ) are more predisposed but I have never heard of it being an individual genetic trait that can be passed in families. I think navicular has a genetic component though, but it could be argued that those horses are not so much predisposed to navicular as structuraly less able to cope with the management that can lead to it. If that makes any sense.
I personally would imagine there is a genetic predisposition sometimes involved but I don't know of any research in this specific area.
I don't believe laminitis 'just happens' myself, I believe it's a result of factors/factor that 'insult' the horses system either in the longer term or suddenly that lead to laminitis. Laminitis, I beleive (atm lol) is a symptom of physiological upset in the horses body rather than a disease/condition in isolation.
I don't know of the direct heritability of laminitis as a disease, but insulin resisitance follows a heritable link. The same link as about has an interesting section about genetics of laminitis in it.
In fact this is a great link about research into laminitis in general. A bit sciencey for some maybe but worth a read if this is your thing!
Thanks, and yes it is my thing!!! I was just feeling curious...and a vet mate of mine is treating a pony now. I am a biologist so love the details! Thank you.