I forgot to ask, OP, is your horse off the track or otherwise?
They can have weak, soft, and badly flat feet.
Yep, OTTB's are sadly renowned for bad feet. You don't want to see Pharlap's(famous Aussie horse, was in the museum) feets, if you know anything about feets!
But I believe this is vastly more about 'nurture over nature' - it's not the breeding so much as environmental factors, when talking racehorses(for eg). Horses that grow up & live in 'cushy' paddocks or stalls, often with little exercise(aside from actual training), live on 'high octane fuel', run hard & shod way before maturity...
Unless we take a heap of horses from many breeds, treat them all the same way, and then
conclude that genetics is playing a big part in TB's feet(for eg), I don't think we should assume it is. **That is not to say I believe genetics plays NO
part BTW. Other types of horse hooves may be more likely to suffer in other ways(than say, becoming the 'splat footed, crushed heels common to TB types), but with unhealthy management, regardless the breed/type it will still likely suffer.
And, given good
management, diet, etc, TB's, like any other breed, can indeed develop tough, strong hooves.