On an inclined plane force of friction on a body going upward is $f_s=\mu R=\mu m g \cos \theta$, where $\theta$ is the angle of slope of the road with the horizontal. To avoid skidding force of friction $(f)$ should be large and so, $\cos \theta$ should be large and thus, $\theta$ should be small.
Hence mountain roads are generally made winding upwards rather than going straight upto avoid skidding.