Dogs for horses
I will say my dog is awesome with horses; not a very common breed however; so that would depend on what you are looking for.
She is submissive to the horses; non-threatening - the horses (even the cowhorses) all allow Kim to lie in their pens or chill out with them and they are not nervous or threatening to her at all. She will leave their pens if they say so; or we say so.
She has a long stride and a clear airway so can accompany us on trail rides; we usually go out for about 1-2 hours and she is happy plugging along beside or behind, never leaves the trail, always keeps an eye on us. She is a protective breed, so covers that requirement too.
I would say for a more common breed;
Boxer - choose a dog with the least extreme head you can; hard to breathe through the pushed up nose - but they are good dogs that are athletic and the boxers that I've known around horses are quiet and respectful, but as a rule they are bouncy, happy dogs.
Dalmatian - be very careful of temperament - Disney ruined this breed - as OC says; look for a working breeder that deals with horses if you can.
Doberman - good dogs again; obedient, watchful, stay away from the extreme chest; you want a conformationally balanced dog - they are more serious than the Boxer
GSD - be very careful and get an extensive health guarantee - HD, Pano, Osteoporosis, Epilepsy, Spinal Myelopathy, no drive, too much drive
Collies, aussies, ACD, BC - horses are not designed to be "herded". They are too flighty and delicate a critter - if you can't train your collie type to leave them alone - and provide them with another outlet for that drive to herd; I would leave this group alone. All ACDs, BCs I've seen on horse farms are either being yelled at constantly or are bothering the horses to no end.
I don't know any schnauzers, bouvs or black russian terriers; but they could probably keep up with the horse, would be more interested with protecting you than hunting (possibly).
Can't think of any more breeds I would like to have as horse dogs; but will say I have had the joy of riding with my stone cold APBT Indy; and he was a great dog to ride with; very respectful and obedient - but you'd have to find a cold one; and no guarantees with pups.