One of the main objectives in any riding/training program has to be to teach a horse to stay 'between the rider's legs' and 'between the rider's reins'.
When a horse starts to do what we call 'rubber-neck', you lack 'shoulder control'. A horse does NOT have to follow his nose (as you have found out) -- he follows his shoulder. So, in order for a rider to get a horse to follow his nose and stay between the rider's legs and reins, it is shoulder control the rider needs to work on. With this training comes the 'lightness' and 'responsiveness' every serious rider desires.
What teaches a horse to 'rubber neck' is a rider that uses a direct rein to ask a horse to turn. When the horse does not turn, the rider pulls harder on the rein and the horse just bends its neck around and still not not turn like it was asked to.
To correct this, DO NOT pull harder on that inside rein that the amount of contact it takes to barely see the corner of the horse's inside eye. Any more bend than that only puts a horse's weight and energy into its outside legs and shoulder and actually encourages a horse to move into the shoulder and away from the direction being asked for.
Instead, once the horse's head is pointing the direction you want it to go (usually with a loose inside rein at this point, put ALL pressure on the outside to PUSH the horse instead of trying to pull it. If a horse is obedient enough to a rider's leg (which most are not if a rider is having this problem) the rider can reinforce with a crop tapping lightly on the outside shoulder, which will be bulging at this point. The outside rein needs a light contract to prevent a horse from turning its head too far and needs to steady the horse, but it is the outside leg or added outside aid that needs to 'make' the horse follow its nose.