Several tours possible linking the high points of the main Teesdale road (B6277) at Harwood (parking at 590m), the Langdon Beck to St. John's Chapel road (summit at 635m, steep bits on both sides), Swinhope Head (Newbiggin to Westgate road, very steep on north near the 607m summit) and the B6278 Eggleston to Stanhope road at 511m and the most likely to be passable. This gives three sections between the four roads, with the best skiing furthest west. However, the minor roads are not ploughed, in which case access is by skiing up the roads, itself a pleasant way to gain height.
Typical skiing on the Tees/Wear watershed 
(Skier: Richard Harrison)
For practice - it would be well to mention the uplift
facilities on the Tees/Wear watershed.
Harwood Ski Federation, on the County Durham side of Teesdale Head,
have two parallel rope tows giving c 50m of uplift and serving two very
gentle slopes separated by a slightly more entertaining gully. Plans are
afoot to use National Lottery money to build a real tow similar to the
Carlisle Club's.
Weardale: on the Westgate side of the Swinhope Head road, two tows
serve a steep NE-facing bowl which looks more suitable for alpine skiers than
nordic. The access road is tiny, and not ploughed with any urgency, though I
guess that it will be cleared as far as Swinhopehead House once the thaw
starts.
Carlisle Ski Club, on the Cumbria side (Tyne Head) have England's
longest proper ski lift, a Poma giving 90m of uplift and serving fairly
gentle slopes which can have delightful skiing. However, the Carlisle lift is
only run on about a third of the days of the Harwood tows, because Harwood's
gully holds snow much better, and the road on the County Durham side is
typically ploughed clear before the Cumbria C.C. have even thought about
clearing their side from Alston. On the other hand, CSC do have
a web site which contains a page
reporting snow conditions which seems to be updated in a timely fashion, but
not a lot of information about costs or membership.
The Carlisle Club tow, 1995/6
All of the hillside between the Harwood and Carlisle lifts is skiable, and away from the tows and the road, has an air of wilderness, with excellent views to Cross Fell if clear. Equally, it can be an awful place if it is misty and thawing!
Looking across to Cross
fell at sunset
Hamsterly forest is sheltered and should offer nice easy langlaufing if the snow line is low enough. There are several bridleways, odd footpaths, and various other forest tracks that are open to the public. However, the author's experience is that quite a bit of snow is needed to make skiing the rather gravelly tracks pleasant. I think there is a charge for parking in the "official" places, but quite often you can't get to these in the snow anyway, and there are perfectly reasonable places to park just a little further away.
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