Always assume it's a medical issue? Interesting. You must have some deep pockets!
Fortunately the majority of the vets at our clinic own and even compete with their horses. The first thing they would ask in this case is what have you tried so far and what was the reaction to the attempts.
I actually agree with the first post. You don't always have to call the vet though... I definitely do not have an endless supply of money to do this. There are several things you can do to check for pain yourself. The first is observation. Is the horse stiffer when he comes out and then warms up out of it (arthritis), or does he get progressively worse as he is exercised (injury)?
If he is always equally stiff, run your hands down his back and neck to check for muscle tightness. Give him a massage, do some stretches- does it help? Does he flinch when you apply steady pressure down along his back?
Check the saddle. Make sure it isn't pinching, bridging, rocking, or pressing on his withers.
Look at his stance. Does he stand crooked? Are his feet flatter on one side than the other?
Even look in his mouth. Feel for sharp edges on his teeth or ulcerations on his cheeks. You may not have the expertise of a vet, but you can spot major issues, or get a feel for if the vet is necessary.
After you have exhausted all of your own resources, if you still feel that this may be a physical issue, then it is time to call the vet. If not, suppling exercises on the ground (carrot stretches, tail pulls, and stretching each leg- make sure you know how to do this properly) and finally under saddle can help. If I feel my horse begin to lock up on me, I find it very benificial to stop, take a break, and then gently suggest that they bend their neck back to my leg around 3 times in each direction. Then when you start going again, if you feel the same stiffness start to occur, apply the same aids. Your horse should begin to bend the neck, at which point you can stop the aids and continue foward. Leg yields and spiraling in and out on a circle are good for the horse that is stiff through the ribcage. Also lots of changes of direction can prevent Your horse from locking up on you.
Hope this helps!