Yes, JeffB, they were indeed re-introduced, which would mean that, if the location 'near Oldham' were to have any connection with mountain hares, it would have to have been introduced to the song after the re-introduction. But I'm more inclined to believe now that it may after all have arisen as a mis-hearing of 'Howden', which itself was a localisation of the original 'Mansfield'. In which case the hare must have been an albino, and therefore a remarkable phnomenon in the eyes of the hunters. I'm probably over-thinking this!

The local population of mountain hares is declining, but I still see them quite regularly up on Bleaklow and Kinder.