All good stuff above!
Arctic hares are lepus arcticus, the biggest of all hares, and are not found here - ours are mounatin or white hares, lepus timidus (subspecies scoticus) slightly smaller than brown hares, lepus europeaus.
There are irish subspecies of mountain hares too - hibernicus.
Here in Saddleworth, the white hares have spread from release in the Peak district, where they are monitored, and are well seen,as has been mentioned, above Dovestone (soon to be an RSPB reserve), and are best spotted on a sunny day, when they love to warm themselves on the rocks,especially on the left as you go up towards Chew res. Not the right, its not sunny enough!
All along the dovestone ridge is good and behind Alphin Pike/Indians head rocks - they are mostly near rocks, so although they get over towards Stalybridge Country Park area, they are scarce there as there is not so much rock as moor.
They may well still have some bits of white coat now, but the boxing will have still been seen in april, may is a bit late for that I think.
Oldham Countryside and Tameside Countryside do hare spotting walks earlier in the year.
Wonderful, wonderful creatures.
Hope this helps, good luck!
Cheers
Ken