Saddlebred/Arab crosses, also known as National Show horses, are primarily bred to be english saddleseat horses. Most "half arabs" that you would see at Arabian shows in english pleasure classes are saddlebred crosses. I work on an Arabian farm and we've had a couple of half arabs (saddlebred crosses) in for training and from my experience with them and ones I've seen at shows they tend to be pretty hot. I'm not a huge fan of saddlebreds based simply on looks but I've also met quite a few who were pretty neurotic. That being said, I've also met a couple who were super sweet and easy, just depends on the horse! I will say they can be very impressive movers too!