A good, well trained chiropractor is an invaluable addition to your horses care when needed.
I ask about education, successes and failures in their career, and goals for my horse. I insist, with one exception, on using chiropractors who work under the direction of a vet. The vet doesn't need to supervise the session, but I want a vet's input on the chiropractors overall practice.
When I ask about their experiences I do it in a conversational way, not grilling. If anyone involved anything's health can't give any disappointments, they are either lying, haven't much experience, or have poor clinical assessment skills.