California 8 year old MFT Gelding, working in riding ring and trails, Snaffle and Dressage saddle. Medium Level Rider

Question: My horse gaits well, he will work trails or in the ring fine. The problem I am having is that when I work him in the ring, he wants to hold his head off to the right. He does this both directions of the ring. I have had the vet check his teeth, he said there was no problem. I have checked the bit, it fits him and is in good shape.

What can I do to correct this problem?

This is certainly one of the most common problems, as almost all horses are stiff on one side and hollow on the other.  The cause of the horse being hollow on one side is that he does not want to accept the bit on that side. This will take a while to overcome.  To straighten him, you must keep working to make him accept the bit on the hollow side by taking a light feel of the right rein and then give little tugs on the left rein to straighten him. 
Remember the cause of the problem is that he wants to avoid accepting the bit on that side, so he must be taught to bear the rein on the right and not avoid it.  Also, it's helpful to spend about 10 minutes of a lesson riding him in circles and serpentines using only the left rein - and then repeat the procedure using only the right rein.  While doing this, part of the time you will be using an opening rein and part of the time you will be using an indirect rein.  Work as smoothly and softly as possible. 

Nancy

Some horses tend to be one-sided, just like some people are right or left-handed.  If he carries his nose to one side no matter which direction you are turning, this indicates to me that this may be a habit he has developed, rather than a pain response (you may want to have a horse chiropractor or massage therapist look at his back to be sure this isn't 
related to pain).

There are a couple of things you could try which may help to straighten your 
horse.

First, try working your horse in small circles, both to the right and to the left.  Spend a little more time circling to the left.  Each time you turn to the left, ask your horse to bend more (turn his nose & body in a nice curve to the left).  If your horse can't bend at all to the left in a small circle, you will need to start with some ground work to help him out. 

With just the halter on the horse, gently pull his head toward his shoulder, first to the right then to the left.  Pull slowly and urge him to stand still.  Pet & praise him for standing still and just moving his head & neck.  All you are doing is stretching his neck muscles.  When he gives easily to both sides (this is called doubling), tack him up, stay on the ground, and 
pull his head in each direction with your reins.  Work slowly & gently until he gives readily in either direction.

Now mount up & try to pull his head towards your knee on each side.  It may take a few days to get him relaxed and doing this quietly.  Pet and praise him for even small amounts of head movement toward your knee.

Now go back to riding in small circles, mostly to the left.  Whenever you are riding and he starts holding his nose out to the right, quietly go back into a  small circle to the left until he is relaxed and then continue on your way.  It takes a while to teach your horse to follow his nose, but have a little patience and you will get there.

Laura

To solve  the head cocking habit under saddle, I would put the horse back in a snaffle (a D ring, an Eggbutt or a full cheek would be my preference) and teach him to bend.  First teach him to go on even, light contact on the snaffle bit in a straight line, even if he does cock his head.   If necessary take a bit stronger contact with your left rein to keep his head as straight as possible. Then try  basic dressage exercises in both directions, first 
riding him into the corners of the arena, pushing straight into his side with your inside leg (thigh and calf) while taking slightly stronger contact with your  outside hand, bending him around your inside leg (the one toward the center of the arena). Be sure to lightly press with your outside (rail side) leg just back from its normal position to keep his haunches from straying too far toward the rail. This exercise will help him bend his entire body, which is the real culprit when he cocks his head and neck to the right.  
 
When he can do decent curves, start riding large (60ft) circles, again using inside "leg to outside hand" to bend him, this time supporting the outside rein with the inside one, taking even contact with both reins.  
 
Retraining  a horse with this sort of bad habit takes time and some skill.  Try to take some dressage lessons to learn the basics of how to do these exercises, then practice, practice, practice.
 
Lee Ziegler