I think many things, might determine whether or not a horse or breed is more intelligent. Or at least 'intelligent' by our standards.
Certainly, draft breeds on the whole, are more unflappable. This because of their use in the past. When they were used for farm work, farmers certainly didn't want a horse who would flip out when pulling a plough, for example. So because of this, the wild ones were seldom bred. Through the generations, with only the most calm and reliable being bred, it was obvious that entire breeds became more calm and reliable.
In Gypsy Horses, all had to be very calm and reliable, since they travelled the roads all their lives, pulling incredibly heavy and expensive caravans, holding everything the family owned. Even foals had to follow along, without running off or spooking at things along the way. They had to be tethered by the side of roads in the evening to graze and with often the young children looking after them. They were members of the family with often, many young children, crawling around the camp. No unreliable horse was kept or bred. So through selection, Gypsy Horses today, have mostly become quiet and sane, easy to handle and reliable.
Wild horses, have their own brand of 'intelligence'. They must learn when wild animals are about, when to safely graze and when to flee. The young learn from their elders.
Without doubt, the more proper training an animal has, the more he might appear to be intelligent. Training makes an animal think. Gives him a sense of responsibility, for want of a better word. Take two litter-mate puppies. Both are showing very bold personalities. Put one in the back yard alone all his life. No interaction with other animals or humans. Take the other and thoroughly socialize and obedience train him, make sure he has enough exercise and give him a job to do. The first dog to many, will appear 'dumb'. He doesn't know anything, probably bites without provocation and barks and digs all day. The second dog, will appear intelligent. He knows his manners, is reliable in all circumstances and safe around visitors and other animals. Neither dog was necessarily more intelligent. It had just been brought out and directed properly in the second.
It is the same with horses. Well trained horses, often will cost more. Somebody has put time into them. Often, lots of time. We must be willing to pay for that. Every day on CL and elsewhere, we see tons of ads for unhandled, untrained horses, for little money or free. Somebody didn't care enough to bring out potential and all animals have some potential.
I do think, just like humans, some animals have more potential to learn, than others, so we must adjust our training, go slowly and not ask more of them than they are able to give. Again, genetics and careful breeding, will have made a difference.
How animals react and their appearance of intelligence, is almost always, their background (genetics) and training - or lack of it.