Horses can, indeed, have "head pain" ----- if the Atlas bone needs adjusted.
I know this because it happened to a Walking Horse I once had.
He suddenly couldn't hold his gait under saddle and would break into a trot (trotting is more comfortable for them when they are in some sort of structural discomfort).
This horse's sacrum and Atlas bone needed adjusted. It was the equine chiro who told me horses do suffer head pain. Some can tolerate it fairly well, others cannot and result can be bad or violent behavior.
If the horse's owner truly believes the horse is having headaches, she needs to stop being cute about it and have a chiropractor evaluate the horse, then eliminate the source of the pain ----------- provided the pain really is there.
My apologies to the OP. I am not trying to Shoot The Messenger; just trying to convey the seriousness of the issue, if the owner truly believes in what he/she is saying