Rescue volunteers were called out to help motorists stuck on the Buttertubs Pass last night.
Members of Swaledale Mountain Rescue Team came to the aid of the occupants of several vehicles.
Heavy snow and high winds had caused drifts on the exposed route between Swaledale and Wensleydale.
The motorists have been criticised on social media for putting themselves at risk by attempting the road.
Officials have urged people to only travel if necessary this weekend.
North Yorkshire Police is urging people, if they do need to travel to be alert to the conditions, drive accordingly and leave extra time for their journey, checking the weather forecast.
Inspector Amy Hunter from North Yorkshire Police, added: “Due to the high level demand in calls for service there may be a delay when calling the police on 101.
“We ask members of the public not to ring 999 if you can’t get through on 101, please leave the lines free for genuine emergencies.
“Thank you for your patience and understanding while we deal with the effects of the storm, and please stay safe.”
In addition to overnight patrols and treatment on main routes, highways teams had pre-salted Priority 1 routes and have been re-treating those P1 routes where necessary and then moving on to our Priority 2 network.
Highways teams along with farmer contractors have been busy opening roads due to snow and responding to almost two hundred reports of fallen trees.
North Yorkshire Fire and Rescue has attended and supported the community at around 50 incidents.
The majority of these incidents included falling trees, power lines and dangerous structures.