This could be down to allergies, but if it is, it would most likely be seasonal and not all year round. If the horse always shakes his head, I would suspect that the trigeminal nerve might be irritated by the bridle.
This could be the result of pressure on one side of the face from either the buckles sitting on top of each other or sitting too high up on one side of the face. It could also be cause by jaw restriction from the noseband being too tight.
The most common reason why a horse would rub their head on you after exercise is because their muzzles go numb or itch due to an ill-fitting bridle that puts pressure on their facial nerves. Other reasons might be sweating, a skin disorder, to assert dominance, mange, switch itch, midges or flies.
This could be a result of poor schooling or level of schooling and lack of strength. However, it could be the result of excess tongue pressure or a tight noseband restricting the jaw movement and therefore impacting the hyoid apparatus and consequently limiting the horse’s movement.
This could be the result of excess tongue pressure, excess poll pressure or pain from the bit.
Drawing the tongue back, putting the tongue over the bit or sticking it out to the side, are all usually attributed to excess tongue pressure. The horse may also put his tongue over the bit if it is too low.
Some bit materials, such as rubber, dry the mouth and therefore stop saliva being produced. Uneven saliva can be caused by pressure points on the side of the face by the bridle. Excess saliva is usually a sign that the horse can’t swallow properly. This can be the result of excess tongue pressure or a tight noseband restricting the tongue and jaw movement.
This is often the result of the bit being too high or too low in the horse's mouth.
This could be related to rider ability but is often the result of tension in the TMJ and/or hyoid due to an ill-fitting bridle, tight noseband or excess tongue pressure.
This could indicate an ill-fitting bit putting too much pressure on the tongue affecting the horse's ability to swallow or catching the genioglossus. Alternatively, it could be the result of a heavy-handed rider.
Flight is a horse’s natural response to psychological or physical stress or pain. It could be the result of an ill-fitting bit or bridle causing extreme discomfort or conflicting signals. However, there may be other issues going on here which might need further investigation from other professionals, such as a vet.
Rearing, bucking or kicking out are very often pain related. It could be the bit or bridle, but it may also be the saddle, girth, or some other injury. If the pain is not relieved through correct fitting of the bit and bridle, I would recommend the rider seek further advice from a saddle fitter, physio, or vet.