Not a western judge, but, as far as I know there aren't any dress rules for judges (but check the rules anyways). For me (dressage judge) basically business casual seems to work well. Mid-long skirts, pants, even knee length shorts work well. And when it's hot many will end up in a nice v neck tee or other work appropriate shirt, no jacket. Basically if I would wear it to the office, I consider it OK for a judge at a show. Many FEI (international) judges dress much the same, and we've had some in jeans in recent years!!
They say money doesn't buy happiness -- well happiness doesn't buy horses!