Clodagh
Playing chess with pigeons
Shagyas are wonderful, but they are tall. If you want an old style arab, then Iranian Asils are predominantly old style desert horses, though some do have a bit of dish.
https://s-media-cache-ak0.pinimg.com/736x/d8/12/1e/d8121ebbd210f436e9c63327e25afebb.jpg
Of course the Crabbets are still fabulous horses.
A friend of mine breeds Arabs (in a tiny way) and she has a Russian mare who I like a lot, also a Crabbet. Bred to do what they should be doing! I am not keen on that Iranian one in the pic.