Actually, it really means that a Dragonborn needs something stronger than a horse.
A RL horse should carry no more than 20% of its bodyweight, or so. A charger or horse with similiar bone-density can hold a bit more, but not a lot. Clydesdale and similiar draught-horse breeds made good warhorse base stock, due to size/density and stamina.
You'll be damnably lucky to find a horse that can carry a 270lb weight for long, and once you add tack and gear, you're going to be breaking that horse.
Sooo.. Dragonborn needs bigger/different mounts. Its not a problem with the Mounts carrying capacity.
Dragonborn are also freaking huge, the average weight being 120kgs.