I've read that racehorses out of that period have less a family tree than a flagpole, and that since no one back then had an inkling of Mendelian genetics, it was all pointless or worse anyway.
That makes sense because most of them came from animals who had to be imported and there were limitations on those imports by the sellers, IIRC. Clydesdales got like that later when they started focusing on offspring from just three stallions.