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.

Related Questions

How dangerous is an internal hordeolum to you?

Not too dangerous. Caused by infection of small glands in eyelid but occuring on the inside of the eyelid r/t outside surface. Often requires antibiotic and excision if internal location. Should not be ignored and you should see an opthalmologist for evaluation and management.
Not dangerous. Internal hordeolum is a clogged oil gland of the eyelid margin. It is not an infection. It will usually drain or go away on its own. Worst case it may become a cellulitis (very uncommon, but needs treated) or skin infection, or a nodule in the eyelid that will have to be removed surgically.

If a stye occurs inside the eyelid, it is called an internal hordeolum. How dangerous is a internal hordeolum?

Not very. These usually cause the whole lid to get inflamed for a while, and then localize at one point in the internal lid. There is no danger to vision or the health of the eye. It would be rare for it to even affect the basic lid structure although they can be uncomfortable and ugly looking.