While I don't believe that laminitis itself is hereditary--I believe that the predisposition to it is. For a long time I didn't think there was anything in that theory--years back I was told that by a long time & very outspoken Morgan breeder. She said that one certain line of Morgans was very prone to founder--she lives in an area that has a large population of Morgans and has been in a position to watch what becomes of a lot of different horses, and she insists that this one particular line has a much higher-than-normal tendency to founder. When she originally told me this, I pooh-poohed it and like Kay said it was just all in the management of the horses, etc. etc. However, in the years since then I have taken note--again in the Morgans, I've seen where a farm using a badly foundered mare as a broodmare--they sold her foals to various farms across the country and within a few years a number of them were lame and put to sleep due to severe founder (and yes, the mare is of that particular breeding). Perhaps it is coincidence that different farms would have just the one horse founder--the one horse they own off that one mare--but any more I am skeptical that it is only coincidence. I really believe that in many cases there is some weakness in the horse that causes it to founder when no other horse on the place is likewise affected--even though the other horses may be subject to the same conditions as the horse which develops laminitis (over-rich feed, excess weight, spoiled feed, whatever the trigger may be)--and that weakness is hereditary. What the specific weakness is I don't know--maybe weak hoof structure (hoof may look perfectly normal, but simply isn't strong enough to stand up to certain stresses?)
I don't believe that all foundered horses have a genetic predisposition to it. Sometimes horses do get a severe overload (feed, weigh bearing after an injury--think Barbaro--infection due to retained placenta) that is likely to cause laminitis in any horse. In some cases, though, I do believe there is a hereditary factor.