Brenda Imus provides a thorough explanation of how to analyze gaited horses' conformations to discover what 4-beat gait they are naturally built to perform.
I don't believe the tail itself has much, if anything, to do with the gait a horse performs, or their ability to work strongly off their haunches. The driving force for the strength in the back end belongs largely to other groups of muscling in the back-end, including the abdominal muscles.