Iron deficiency anemia symptoms explanation
The molecular basis of copper-transport diseases in Trends in Molecular Medicine, Volume 7, Issue 2, 1 February 2001, Pages 64–69, has a link to a 1973 paper by JM Gillespie entitled "Keratin Structure and Changes with Copper Deficiency," stating


  Menkes patients are often diagnosed from their unusual hair structure – termed pili torti – also known as kinky or steely hair, caused by reduced keratin cross-linking, a process that is catalyzed by an uncharacterized copper oxidase.


I haven't been able to find anything further, but since iron and copper levels can both be affected in anemia, this may be the link you're looking for. There may also be other enzymes involved that use iron-mediated catalysis. Since there are so many different kinds of keratins (the major protein that makes up hair and nails, among diverse other functions in the body), there may easily be multiple cross-linking and assembly pathways.

Other websites I found have also claimed that anemia-associated pathologies with hair and/or nails may be related to reduced oxygenation as a result of low iron levels, but they don't give any citations, and given the nature of the sites (nail care, fashion, etc.) it may just be an educated guess.