I don't quite understand why you would want your horses head to be higher. In my opinion a naturally low head set is a really good thing, a lot of people would love to have a horse like that. But, you could train your horse to keep his head higher if that is what you want him to do.
The important thing really is not his head, but how he uses his body. From the second picture it looks like he has a bit of impulsion, but he could have more.
Seat to hands means using your leg and seat to engage your horse's hindquarters. By encouraging your horse to use himself by pushing off his butt, he will naturally become more round and supple.
QH also naturally have necks that tie in low to their shoulder, compared to warmbloods and thoroughbreds that have necks that tie in higher. They will have a higher headset than a QH because of this. Your horse might not be capable of carrying his head the way you are describing. But agian, that is not really the important thing.
So try not to worry about how high his head is! He's a very attractive little horse! Maybe taking some dressage lessons will help you understand how seat to hands works.
Agree with what MLK11 said. Also, by engaging his hindquarters, he will bring his back legs under him more and give him more of an 'uphill feel. I would use lots of bends, transitions and half halts to encourage him to engage his hindquarters and round through his back - this will then communicate to his head and neck and you will get a better head carriage.
You'll probably never be able to get a 'classical' dressage way of going, but if you don't show or do dressage it doesn't matter!
I have a paint that I train for WP. Not only does he have a naturally low headset, he also has a pretty thick-but-long neck. This causes problems when it comes to collection. :) Good for you for not wanting to just pull his head up!
Here's his 'low' head position:
And that's where he likes it. :) But in order to get him in shape for WP and Huntseat, I work him 'up' like your describing, like so:
Not our best picture, but I'm sure you get the idea. ;) His head set comes up a little higher with consistent, careful work.
The first thing you'll need to do is carry a dressage whip (unless your boy likes going forwards). Start at the trot (the walk will be the hardest), and push him into a really nice purposeful trot. Not something that /rushes/, think of big, long, powerful steps. Do NOT lean forward. The moment you do, your horse is going to go, 'why bring my head and chest up if she just leans on it??' Usually, when you push your horse forward, his head will come up.
...And, it might only stay there for a few strides, because he thinks to himself, 'this is a lot harder then what we used to do!' Not only does he have to learn to push off his hind end, but he has to OVERCOME his conformation and pick up that head and neck. When the head comes down, use your legs first to encourage him and the dressage whip ONLY if you have to to get him to bring his head up. Only work on this a few minutes a day, and only when he's fresh (asking him to do it after he's tired is mean and you won't get what you want!). Stay at the trot and canter in the beginning.
DON'T fuss with his head in the beginning, just make sure he isn't sticking his nose out and hollowing his back by trying to encourage the looong movement, and the long neck forward. Squeeze one rein GENTLY if he locks his jaw up and release when he drops his nose somewhere around vertical. Really don't pay attention to his head for the first couple of weeks though!
As he starts learning his 'new' job, you won't have to encourage him so much. It is hard for them when they start out, but it is possible to get them to carry their head higher with correct work. This is, of course, the simplified version, so if you try it and run into snags, let me know and I'll explain anything further!
OK lets just stop for a second and analyze the pictures. I really like the juxtaposition of these pictures. If we were to take the first picture and rotate it clockwise a little bit and then put it on top of the other horse so that the head/neck line up, we would notice that the first picture has to get rotated quite a bit to get the haunches of the horse down enough that his head/neck would be in the same place. This tells us that in the first picture he is more downhill, and his hind end is not as engaged in the first picture, compared to the second picture.
In order to achieve the higher activity behind that allows the horse to engage his "motor" and bring the forehand up, we must ride from the legs to the hand. This does NOT mean kick and pull. By riding from the leg to the hand, we are starting the engine with our leg and then catching the power from it in the hand and the seat to regulate it. This is where the half halt comes from, and it is mostly through a stalling seat that it is achieved. The only thing the hand does basically is sit there and let the horse come into the contact. To catch the energy from behind with the hand, it just needs to hold the rein and let the horse seek contact, it NEVER, repeat NEVER EVER pulls back, because that is just like putting the gas and the brake on at the same time. And if you notice with cars, just tapping the brake gives a large reaction, while to accelerate, we really need to apply pressure to the gas pedal, the same goes for horses. You really need to gas it to get the energy you want, but the second you touch the mouth, the horse is going to slow down and lose energy.
In your seat you also need to ride really actively with the horse in your neutral seat so that your lower back can absorb the energy and stall it, or redirect it or do whatever you want with it.
I could go on but I have a midterm to write :P So good luck and I really suggest taking some dressage lessons from a good trainer in your area.
It depends what you're riding him for. If you aren't in competition, a low head is a good thing. This is because a horse with his head lowered is in a relaxed state of mind. When a horse has his head raised, this is because he is alert to danger. For safety purposes, many trainers actually spend time getting horses to lower their heads on command. If you are trail riding with this horse, a lowered head is preferred.