Horse does not need any special muscles to lower its' head. Rather it needs to relax the muscles that are literally pushing it out against the pull of the bit, these being the muscles in the front/lower part of the neck.
If the horse doesnt know the cue to lower the neck, then pick a cue and teach it. I use a "tickling" of the reins to ask the horse to reach forward and down.
I was just riding a horse yesterday that needs to learn this, big time. I tickled the reins, asking her to take them forward and down, but she had no idea what I wanted. It will take time, but if I keep doing this, she will try this and that to respond to this stimulus. Eventually, she will just happen to move her face forward and neck down. I will be watching like a hawk for the tiniest bit of that movement to happen. When it does, I will cease any hand movement on the rein and will give the rein forward a bit to reward her.
Rinse and repeat, many times, and eventually she will take the rein forward and down when I tickle them with my fingers. I will not give away the rein totally, but will "follow' her mouth down, maintaining a soft contact.
A person can do this cue training either standing or at a walk. IF you do it standing, then transition to walking after a bit. Doing this WHILE moving forward can be harder for the horse.
Once they are getting it walking, then you keep a little bit closer contact as the horse reaches down and put more leg on, you stay upright and be really free with allowing your hip to move with the horse. All things to encourage the horse to step more forward and under themselves, while with your contact you are asking the horse to step under without raising the head, and to not get heavier on the front. Result will be that the horse must lift up the back and the lower portion of the neck (where it enters the shoulders). This will help to build a better neck and topline.