There seem to be some major differences between the JP's Training Ground mob and drop lists and those of the US's Training Grounds. Example being that Centaurs don't spawn in the Rider Training Grounds, so you can't get Meteor Horseshoes there. The same appear to be true of the Archer Training Ground.
They add more items to the events as they become drops in the singularities. Gears and pages will drop around the time London is out. The horseshoes, we might have to wait until Camelot before they are fully available.