Dennis - I am no expert nor am I a metallurgist . . . that said . . . I would think that the survival of such metal chunks, shavings, etc. would also depend on location and soil types and conditions. I've done some metal detecting, etc. and one has to remember that artifacts from the Rev War (and earlier) are still being found. . . . many of them made of steel/iron and still identifiable as to what they originally were. Although much "newer" that the artifacts you are taling about, Civil War sites still are producing many relics of steel - gun barrels, furniture, shrapnel, etc. (I'm referring to "private owned CW sites).
It would be interesting if you could pinpoint the general area of the forge and then work the area with metal detectors to see if you could locate anything. . . maybe not large pieces but enough to determine if the site is a possibility. A lot would depend upon the depth such things rest at under the surface . . . but nothing ventured, nothing gained. There are a lot of "relic hunting clubs" out there . . . if you could get permission to hunt the area, you might be able to arrange with a club to work it with their detectors to see what comes up. You might not come up with anything . . . you might just find "shavings" and "chunks" . . . but you have to realize that even though such a business would certainly would repair broken tools, etc. . . . tools beyond repair would probably be discarded. If you found something like that . . . or lost personal items . . . . it would give you a clue to keep looking in that location.
Many years ago, when I was a kid, I helped a fellow work an area that he thought was his family's original homestead (in lower Michigan) in the very early 1830's. It took a lot of grid work but we stuck with it and finally located a cut stone indicating a possible foundation. Further digging and work (and a bout with poison ivy and many insect bites) and we uncovered the original foundation made of stone. We found many things such as metal buttons, bone buttons, a jaw harp and probably a half a dozen broken clay pipes. Such things as the clay pipes which don't breakdown even though buried for a 130 years at that time, all help to put the puzzle together.