@Eric Rose
Thank you!
In the XV century in Spain, there was a special court to combat heresy, the Inquisition. Well, actually in those early dates what the Inquisition did was to "investigate" the truly intentions of the jews and muslims that convert to cristianism, the "conversos". I'm sure that most of you have heard some infamous story related to this catholic institution.
The accused in that court has to clothes with a rope that covered his/her chest and back, and wear a cone in the head. As he was accused of a "sin", to wear that custome was a kind of penance that embarrass the person.
To take part in one procession in the Holy Week is also a penance, thats the reason why the groups that form the procession, "cofradías", use that kind of clothes even in that early times.
Cheers
Antonio