I'm glad you quantified that with the word Iodoine! Recently while painting a focal wall a dark rich raspberry color my pure white dog brushed up against it and became Pink Dog, it's wearing off now..but he did get 'painted'.
I think that's a great question though..and I would certainly paint my dog with Iodine if the need ever arose. He's kind of hairy though, but when wet it quickly shows his skin underneath..so it wouldn't be difficult to paint my dog. He does have one spot on the top of his body near the back end that is really a small lump, has been there since he was a puppy, and I thought it was from a shot site perhaps. I just keep a close feel on it, for changes and it has not in 8 years. I wonder if I should try painting it? I have to think a bit on that one. I might try it for a week and see what happens. He does get Iodine in his drinking water 1-2x a week.