Bridle too tight at the poll
Is this horse being ridden? I have seen this problem in a horse before, and it was due to her bridle being always too tight. It seems to be popular to talk about two wrinkles in the lips, even when horse conformation is so different horse-to-horse. The bridle should not be tight at the poll ever! If it is tight at the poll, that means that the bit is exerting pressure constantly, even before you have started to ride. The horse is in constant pain. They can develop a sensitivity at the poll where they would not want to be touched. If the horse is also sensitive at the lips, there is another indication. Loosen your bridle quite a bit. It may take some time for the nerves to heal, and for the horse to forget its pain. Really, it is just important that the bit is not so loose that it bangs against the front of the teeth, but generally a horse will carry its bit anyway. There is no advantage to a tight bridle. The horse will not be able to feel your hands with the mouth if the bit is already tight. You will only be able to affect the neck in this case, and the horse will always be hard-mouthed. Good luck!