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.
The weather problem needs to be solved if you want fully autonomous vehicles with no human on standby, otherwise when it snows you'd have a bunch of autonomous vehicles stood still, blocking the road not knowing what to do.
There are tens of millions of US customers who live in areas that never receive snow and rarely receive rain. It's clear there are a few different technical solutions, and probably the engineers working on these problems will think of a few more in the next decade, if it's a major challenge SDCs will just be targeted at minimal weather markets to start out.
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.