Staithes seems to have its own microclimate: often, it’s sunny and dry while the moors are covered in mist. In winter it escapes the worst of the snow - although being at sea level may help explain that one! - and the main access road - A173 - is usually kept well cleared.
We use these websites to check on the weather: they relate to Whitby, which is a few kilometres south of Staithes, but still the nearest and most relevant weather station:
click Here for Whitby Weather (a local site)
To check the road condition (can be useful in winter if it’s snowing or snow is forecast)
click Here for a webcam of the A169 Pickering to Whitby near Fylingdales
My favourite live webcam, at the Turnstone Gallery at Sandsend, which is a short distance from Staithes (toward Whitby), is currently offline. Here's the next nearest, at Whitby: Click Here to see what’s happening now
I hope these links are useful, please email me if you’d like any more