The Hornpipe was a single-reed pipe, originally made out of a bored cow-horn or similar, and played in various forms throughout Europe and the Middle East; in Wales, for example, it was known as the  Pibcorn,  in Scotland it was the Stockhorn.

More pictures and soundsamples at  Ancestral Instruments.

There seems to be no particular connection, apart from the name, with the dance form.

Malcolm