My boy was very stiff when I met him, and I did a lot of ground work with him. Got him to bend in either direction by offering a peppermint held nearly to his hindquarters (he had no neck muscles), lateral work in hand, driving in long lines, etc. I also massage him before riding, to loosen him up. Another loosening exercise we do is to have him bend his head and neck nearly to the ground and between his front legs for a peppermint (he is mostly good motivated). I also have him stretch his forelegs after putting the saddle on, prior to tightening the girth. My personal feeling is that if a horse is not supple on the ground, he (or she) certainly will not be supple under saddle. He is 22 (I thought he was 24 until I had to look at his papers this week), has a club foot and some arthritis in his back due to falling over backward in a starting gate in his distant youth. Keeping him flexible is a major concern for me, so I seem to spend more time doing things on the ground than actually riding him. When I ride, I carry an mp3 player (external speaker) so he has music to move with, keeping his rhythm and speed constant.
Is your boy stiff because he is simply not relaxed or is there some other cause? Have you tried a chiro or massage therapist? Mine (massage person) suggested rubbing lavender oil under his throat and lower jaw for relaxation and using a sports rub of epsom salts and rubbing alcohol to loosen his muscles. It really has helped a lot. I put a warm towel over his back with the rub stuff for about 20 minutes before saddling. Since he was a racehorse, he is used to people doing strange things – my mare would not stand for that nonsense. You could try some or all of this, and perhaps it will help.
It is never the horse's fault