Derbyshire County Councilhas just put up some publicly available webcams too. So far they are mainly in the southern part of the county but a very useful one is on the A515, between the Monyash turn and the Bull i' Thorne, which is the notorious spot for the rosd to get blocked when it snows.
The link is:
https://apps.derbyshire.gov.uk/applications/traffic-cameras/traffic-cameras.asp?camera=monyash
Maybe they will put some more further north around Castleton and Snake Pass.
