In reply to Bee_1:
We were up in Langthwaite (just beyond Reeth) last weekend and the roads were very clear.
There was a fresh dump of snow on Monday but the roads were still OK yesterday and it's expected to warm up tomorrow, so I doubt there'll be a problem.
Even if there is fresh snow, the locals told us that the main road from Richmond through to Reeth is always ploughed and gritted, so if you stick to that and avoid the hillier routes over from Leyburn (assuming you're coming from the East), you should be OK.
And you could always phone one of the pubs in Reeth or your bunkhouse if you're still worried.
FWIW, we'll be heading up to Langthwaite this weekend too...