Everyone working on autonomous vehicles is facing a similar issue, and it's also one that human drivers are pretty bad at. Most people solve it by not going outside as frequently with snow on the roads.

Tesla's goal is high fidelity GPS mapping of roads and their landmarks, so that the car can navigate down a lane in the absence of normal visual signals (i.e. clear road markings). It will be interesting to see how everyone else deals with weather conditions, but it's also not a problem that needs to be solved instantly.