Many of the local roads become impassable in winter due to snow and ice.
Kirkstone Pass is often effected, and signs are put up to say so. However, lack of a road closed sign isn't a guarantee that the road IS passable. AND a 4WD is not a guarantee of a safe passage either. Many modern 4WD cars have tyres that are not design to grip in snow or ice.
Other more remote roads are more likely to be affected since it is impractical to grit them. Wrynose and Hardknott Passes are often impassable, sometimes due to significant icy patches.
You can't blame your sat-nav. It can't tell you anything about road conditions. Only you eyes and common sense can provide that kind of information
Winter driving advice is particularly relevant in mountain areas. See RAC Patrol Tips for Winter driving.
If emergency services are aware that you are stuck, stay with your vehicle. If you decide to leave your vehicle for any reason, walk along the road towards civilisation. Don't cut across country, even if it looks like a shortcut.