But there is no specific regulation that sets a minimum visibility for such an arrival.
Provided you hold a valid IR!
That is why I did not include reference to IR holders in my original post. If you don't have an IR then the other limitations will apply.
Whilst it may be legal to fly a visual approach under IFR! it goes against the basic principle of never flying IFR below the Safety Altitude unless on an Instrument approach or departure.