It's pretty common to school in a double when the horse is ready for it. Double bridles are used quite differently in the saddlebred world than in dressage and it is possible that the dressage riders you have seen and know of are at a different place in their training than I am with my horse.

The double bridle is not used for control nor should it be. I trail rode him in the double because my snaffle bridle was not with me. As long as he was comfortable, I think that's all that matters. YOu can scold me more about it when you have ridden dressage, ridden my horse or spoken to my instructor. Your choice.