I don't know if it is common, or I just had luck, but I watched in Escorial a very interesting parade.
Clearly, it was the real people, here and there with very naif details, but always with the Spanish garb.
It's interesting to check when do they happen, this pilgrimages.
The Escorial itself was dedicated to Saint Lawrence (San Lorenzo), presumably to honor the Spanish victory against the French at San Quentin, which took place on the Feast of St Lawrence on August 10, 1557.
Who then was San Lorenzo? He was the third century martyr. He was the custodian of the chalice, the cup that Jesus and the Disciples drank from at the Last Supper. San Lorenzo was martyred by burning "grilling" hence his association with a gridiron.
Interestingly, Phillip II sought to include this gridiron motif in the design of the Escorial. The Initial architect was Juan Bautista de Toledo, a Spanish architect trained in Italy. The completion of the project was by Juan de Herrera, an apprentice to Toledo, but not a trained architect as such. He was apparently a man of enormous and varied talents, chief among them being able to communicate and satisfy the very particular design desires of Phillip II.
Every year, the second Sunday of Septembre, there is a Romería (pilgrimage) to this beautiful Ermita (Hermitage) which is in La Herrería).