The 2nd photo on playmodb of the box back is from the era where they just liked to make a nice scene. I believe the boy with the hat is from the organ grinder set especially since the girl is in there too.In the individual parts the boy is shown as wearing a hat but I think the picture is just meant to represent the figure and not any accessories. It looks like that picture was just cut from the one above.I'd say no hats in this set.
My sister owns that set, and theres no kid with a hat in it. Seeing how we never had any victorian style hats for boys, I am 100% certain.