Although some behaviours may be extreme, I have not yet met a horse I couldn't help.
If a horse is misbehaving due to pain (back, tooth, ulcers etc) then the horse must be treated before I will work with him. In these cases the behaviour initially presented as a response to pain can become a learned behaviour and can continue even after the pain has been addressed. This is what I would work with.
I truly believe that no horse is 'untrainable', unless in the very rare case of a brain tumour!