What are good exercises to make the horse more supple?

Suppleness is the quality that separates a horse that merely goes through the motions from one that is genuinely through, connected, and a pleasure to ride. A supple horse swings through his back with each stride, bends uniformly through his body on curves, yields easily to leg and rein aids without resistance, and carries himself with a relaxed elastic quality that makes the work feel effortless from the saddle. That suppleness is not a natural state that some horses have and others do not — it is a developed quality that emerges from systematic gymnastic work applied consistently over time. Transitions are the single most powerful suppleness exercise available and the one most riders underuse because it seems too simple to be the answer to a complex problem. Every correct transition — upward or downward, between any two gaits — asks the horse to engage his hindquarters, adjust his balance, and move the energy through his body in a way that develops the throughness and connection that suppleness requires. Ten minutes of frequent correct transitions develops more suppleness than forty minutes of sustained work at steady pace, because sustained work allows the horse to go on autopilot while transitions constantly demand reorganization. Circles and serpentines are the foundational lateral suppleness exercises. A correct circle requires the horse to bend uniformly from poll to tail in the direction of the arc — the ribcage swinging toward the outside, the inside hind stepping under the center of mass, the hind feet tracking on the same arc as the front feet. Serpentines amplify the benefit by requiring the horse to change his bend repeatedly, preventing one-sided stiffness and progressively loosening the topline in both directions. Leg yields performed correctly are among the most immediately effective suppleness exercises because the crossing hind leg must flex more through the hip, stifle, and hock than in straight-line movement, developing the range of motion in the hindquarter joints that is prerequisite to collection. Shoulder-in is the exercise many experienced trainers consider the most complete suppleness tool available — the inside hind must step under the body, carry weight, and adduct against the outside hind's track, all while the topline maintains its bend and the horse stays forward and through. Pole work and cavalletti produce immediate visible improvement in trot quality and back swing without requiring specific training pressure from the rider. A horse trotting over poles must lift his legs more actively and regulate his stride with precision that flat work does not demand, developing the hip and stifle flexion and the lift through the back that are the physical expressions of suppleness. Hill work done correctly is one of the most powerful physical suppleness tools, with uphill work developing pushing power and downhill work developing the rearward weight shift that collection demands.