When the signs and lane markers are covered by snow and ice it will just default to using the same markers everyone else is using; the crashed cars driven by idiot humans who thought they could see the lane markers.
Seriously though, no autonomous vehicle would be dependent on lane markers as the sole feature for positioning, you need to use a multitude of inputs ranging from using markers to using LIDAR to map geometry of the area, through projection of probable trajectories and even to using prior knowledge or map data of the road. You have to have a multitude of independent systems cooperating, validating and agreeing on the most likely model for the current reality. Any autonomous vehicle deemed safe enough to actually operate autonomously should be significantly more capable of reliably assessing the situation than the average human. If any climate presents a difficulty for the detection and navigation part (as opposed to purely physical performance limitations) for an autonomous car it should not be allowed into traffic as it's obviously nowhere near capable enough to trust with human lives.