Could the strength/weakness of a horses chestnuts relate to the strength or weakness of the hooves?

Yes. The chestnut is an "extra hoof" that has no longer been needed through evolution. It just grows on the inside of their leg, and has moved from the hoof through evolution as the animal evolved. It is the same material as a horse's hoof, it just grows in a different area. Usually chestnuts are softer than the hoof anyway, but if it is unusually soft, giving extra supplements for the hoofs should help both.

I suppose it's possible. I own a paint mare with terrible feet. In her defense she has a scar on one coronary band, so riding her without shoes really isn't possible, thanks to the permanent crack in her hoof. But her feet really are substandard, so does it mean anything that her chestnuts cling so hard to her legs that they have to be cut off? Not sure. One other app mare I had years ago had just okay feet, although she was prone to laminitis (easy keeper). Her chestnuts had to be slathered in petroleum jelly for a couple of days before they could be pealed off. I do know that the old belief about white and black feet seems to be grounded in reality-- most farriers admit that dark feet are tougher and harder, although there are exceptions.

I've never thought about that before, but it would make sense, wouldn't it? However, my mare has the toughest chestnuts ever but her front feet chip and wear down pretty quickly. I'll have to check on my other horses' chestnuts, I've just noticed my mare's because they'll get kind of long and not flake off at all.

Good question!!! I'm interested too! LOL You would think so I mean they are both made up of keratin but I honestly think they would have to do studies to prove it. You would think so though!