caracolear

To caracole — a specific equestrian term for a horse making a series of half-turns or a spiraling, winding movement, historically used in dressage and cavalry maneuvers. From caracol (snail), evoking the spiral shape of the movement.

• El caballo caracoleaba nervioso antes de la carrera. — The horse was caracoling nervously before the race.
• El jinete hizo caracolear a su montura para la exhibición. — The rider made his horse caracole for the exhibition.
• Los caballos caracolean al paso de la procesión. — The horses caracole as the procession passes.

This is a specialized equestrian term, not a general word for 'to spin' or 'wander around' — andar/moverse en espiral is what you'd use outside the specific context of horses.