I used to have a TWH, who I did saddle seat with.
To get a horse to hold his head in that high position takes a lot of conditioning, etc. My TWH used to have his nose in the air..
This his him 4 years ago when I first got him. 59620_1413858868803_3491006_n.jpg
And this as him when I truly started to show him, I did a lot of conditioning.
(Yes, he gets SEVERELY sun-bleached! Lol) 148540_1313631780793_3779197_n.jpg
I'm sure you would want it much higher though. My two cents would be to get him going faster and engaged. I suggest leaving stretchies to professional trainers, personally. However in these sorts of sports in riding, I ask that you might want to think about finding a trainer.