‘the horse does not bend when you try to ride him undersaddle’
that’s how i understood your post. that’s what i responded to.
will he turn his neck to the right when he’s turned out, being led, offered a carrot, biting a fly, or scratching his side? can you turn his neck to the right with a side rein set 1 hole shorter, or 2, reins handled from the ground, with a lead rope? what does he do if you tickle his side on the right? how about grazing grass and reaching thru the fence or gate for grass? how about if he’s loose, and another horse comes up on his right?
do you longe him in side reins ever?
does he never turn his head and neck to the right under any circumstances?
often, stiffness is just not having been ridden bending in each direction. the horse isn’t physically unable or in pain, and reaches, turns and bends in both directions in the pasture when loose, but just is not used to doing it under saddle. he may refuse to do so because it’s unfamiliar, not because it causes pain.
other horses are in pain, and have a neck injury that is either recent or old. i used to ride a horse that could not flex at the poll/neck because of an old injury to the atlas (joint between neck and head).
other horses don’t have neck pain at all, they seem ‘stiff’, ‘stubborn’ not because of anything with their neck but because their hind legs are not equally able to manage their weight as they move. often horses that seem ‘stiff’ to one side and ‘won’t bend’ are actually having a problem with the hind legs, not the neck. hind leg lameness or uneven-ness can cause the problem.
a horse may seem ‘stiff’ and ‘won’t bend’ because he’s leaning or ‘falling in’ or otherwise doesn’t have his weight distributed properly.