Head tossing horse that loves to run?

My daughter's horse, who we've had for about 3 months, is a major head tosser. He's seen the dentist, farrier, chiropractor, etc. so it shouldn't be a physical problem. The thing is that when she's riding him in the arena, he starts tossing his head and dancing around and then once she lets him, he takes off galloping like a racehorse!! He'll run non-stop unless you stop him, to the point where he would exhaust himself if she let him (which she won't). But out on the trail, he is a perfect chilled gentleman. I'm figuring maybe he's like this because he's been a competitive horse...? What I'm most concerned about is the head tossing...he gets so carried away, I'm afraid he's going to hurt her. Opinions would be appreciated.