Researchers are working on this in Michigan. The University of Michigan has a new MCity test facility[0], and I know one of the projects they are working on is how the cars handle snow. They basically still do LIDAR and match the z-plane (height of objects nearby) to localize the car when road markings are hard to see.
Still lots of work to do though!
[0]: http://www.mtc.umich.edu/test-facility