I really like the idea that it is a home made defroster heat boaster. Only a cold weather owner would know that.
The engine air intake notion also has validity. Only a little improvement in the height of the air intake, but there is certainly the advantage of the air box that would protect from sucking in water.
Do you have a photo of inside the box? Any evidence of a baffle that might have lived in there at one time?
Ed, I have no recollection of an engine compartment- to-passenger compartment air duct. What year was that? Between my brother and I, we owned a 300d limo, and at least 5 other 1960's vintage fins, S models, and W114/5's. I can not recall such a device. Could the old panton bodies of the late fifties and early sixties have such a device? Seems possbile, if not potentially deadly.