We've had two horses (3/4 sisters to each other) that would NEVER back down from a cow. NEVER. They've gotten charged and hit before, and never moved a step. Those cows learned their place pretty quick. Those mares didn't take any $%!t from cattle. Darn good horses. (Granted, none of our cows have horns.)
And a couple others that would "get you the heck outa here" when a cow even just threatened to charge.
Now I've never shown a cow horse at a show. This is just a matter of working cattle on my parents' ranch. And to me, a truly good cow horse that is bred for it, probably would not have the tendency to back down. I would think they'd have the tendency like our two mares to have a natural ability to be the boss of the cattle, no matter what.