Deviation Actions
Reining - Stamina, Agility
Trail - Temperament, Intelligence
Cutting - Intelligence, Agility
Western Pleasure - Temperament, Stamina
Western Equitation - Temperament, Intelligence
Skijoring - Speed, Agility
Breakaway Roping - Speed
Tie Down Roping - Speed, Strength
Team Roping - Intelligence, Agility
Barrel Racing - Speed, Agility
Pole Bending - Speed, Agility
Gymkhana - Speed, Agility
Halter - Temperament
Liberty - Agility
Dressage - Intelligence
Haute Ecole - Intelligence, Agility
Endurance - Stamina, Temperament
Cross Country - Stamina, Agility
Jumping - Agility, Stamina
Vaulting - Temperament, Stamina
Fox Hunting - Temperament, Stamina
Polo - Agility, Stamina
Jousting - Strength, Temperament
Mounted Archery - Temperament
Cowboy Mounted Shooting - Temperament, Agility
Tent Pegging - Agility, Speed
Flat Racing - Speed, Strength
Steeplechase - Speed, Stamina
Weight Pull - Strength
Log Pull - Strength
Driving - Parade - Temperament, Strength
Driving - Racing/Obstacle course - Strength, Agility
Driving - Dressage - Agility, Strength
Harness Racing/Pacing - Speed, Stamina
Hunter Hack/English Pleasure - Temperament, Stamina
Saddleseat - Stamina
Trick training - Intelligence
Trick riding - Temperament, Stamina
Bombproofing - Temperament, Intelligence
Therapy riding - Temperament, Intelligence
Therapy (non-riding) - Temperament
If your chosen discipline isn't listed above I leave it to you to figure out the best stat applicable. Two at the most.