How dangerous is a hordeolum?

Not much: A hordeolum is an inflammaion of the lid (a stye) due to infection in one of the glands. It can spread over a broad area of the lid as the skin of the lid is loose and not bound to the underlying tissue. If untreated it can go away, but might coalesce into the pus pocket which will eventually open and discharge. If left alone like this it may scar but will not endanger vision.