An iron bow would have to be just about the silliest excuse for a weapon ever. The only way you could use it effectively is if you hit someone over the head with it.
Steel is almost as bad, but you might be able to make one thin enough that it would act like a spring and be effective. Try that with iron though and if you did manage to bend it, it would snap.
You have got to think about it from the perspective of the smith-meister. Depending on your level of skill you'll be more nuanced and thus more capable of creating better weapons. So, when you can only build with Iron you only have enough knowledge to build a hunting bow. When you learn Steel you can build a long bow. (note: hunting bows and long bows actually cannot be crafted, they can only be found) But, it's the knowledge associated with your crafting skill that associates hunting bows to iron and long bows to steel, it's not at all about the material used for the bow.
Wood is much MUCH better for a bow than Iron or Steel. The material characteristics of those two metals is all wrong for bows.
Of course the idea that you can improve a bow using a grindstone and chuck of wood or metal is kind of silly too.