No Quarter Horse has won the Tevis Cup. In 1966, a Thoroughbred/Quarter Horse cross won the Haggin Cup, given at the same race to the finishing horse in the best condition. I haven't found an easy way to look at the breeds of the finishing horses, but it wouldn't surprise me if there were Quarter Horses that finished. read more
There are few riding breeds that don’t have some Arab ancestry, and those known for endurance often have more Arab in them than others. While you can certainly find horses of other breeds that do well in endurance, Arabians and Arabian crosses as a whole dominate in endurance competition. read more
The Anglo-Arabian or Anglo-Arab is a crossbred horse that now also has its own status as a horse breed. It is a Thoroughbred crossed with an Arabian so two of the oldest and favourite horse breeds ever. The best examples of this breed inherit the refinement, good bone, and endurance of the Arabian, as well as the speed and scope of the Thoroughbred. read more
Check out 'Go the Distance' by Nancy Loving and then 'The Complete Guide to Endurance Riding and Competition' by Donna Snyder-Smith - they have details on attitude/body type/how the horse was raised/ etc when choosing a distance horse. read more