I've used a shot glass of iodine after birthing a foal to dip the umbilicus...help dry out and disinfecti would only use it externally - not on mucous membrane - mucous membrane is inside a body cavity such as mouth, bum and vagina - and in chickens - the vent.
i have used it on human belly buttons and here is a quote from a dairy article.
The most common dairy farm practice we have observed is to use one product for all three jobs; cleaning, sanitizing and drying.
Tincture of iodine is nearly universally recommended for these tasks. When used liberally it does a good job of washing off MUD. The seven-percent iodine concentration is strong enough to kill most pathogens with a short contact time. The tincture of iodine
is an alcohol solution. The alcohol acts to dry out the cord tissue. This speeds up the rate of closure.