Iodine does help nails. I once had a horse that came from a previous owner with some hoof problems. The farrier had me mix glycerin and iodine together and paint the hooves every day for a few weeks and they toughened up and were very strong without cracking. After that I applied it about once a week or so for maintenance.
Once when I was a teenager, the optometrist looked into my eyes, then pinched my fingernail and nailbed with his fingers and told my mother I was anemic and to take me to my regular doc for a blood test. I was very anemic and put on iron supplements. Nail health is indicitive of overall health!! Pay attention to them :-)