Please don't listen to others on "headset": the horse always does the best he can with his head & neck for the movement that he's executing with his body! Who but the horse knows what he needs to do with the lever of head & neck, when you think about it? If you read/hear any authoritative words on the subject, they'll say this. I suggest that you read classical literature on the subject & find for yourself that this is so, as well as let common sense tell you that the horse knows best what to do with head & neck.
The horse has difficulty with bad riding (confused signals, harsh hands, etc.), so he's just trying to stay in balance under the onslaught of that, thus his head & neck aren't going to be prettily arched under bad riding. The way to fix that is NOT to force him into a headset, but to LEAVE his head alone, for starters!
Also, the vertical profile is another false ideal: your horse's nose will naturally be in front of his forehead if you leave it alone; & this is therefore to be left alone!
All of the interference for a "headset" only puts the horse on the forehand, thus compromises his emotional contentment & physical soundness.
Focus on your core, legs, seat, weight aids, in addition to your mental connection/partnership with him, which are natural aids for the horse & leave his head alone, for your horse's sake!
Later in your journey, there is the mechanical help of the horse in in-hand galloping, where you help the horse circle his energy & not fall on the forehand in the gallop, but that has nothing to do with a headset: his nose is out in front & you're just aiding him!