LIDAR is supposed to have low attenuation in water, however it will still suffer refraction. Hopefully it will function about as well as a human. The vision processor will have to understand that it's raining and correct for refraction where possible.
Snow is a different challenge, but a sufficiently smart system should be able to composite frames and appropriately fill in the holes created by being obscured by snow. It won't be trivial, but it should all be doable.
