This is one of the reasons why I'm suspicious of camera-only systems, here in Finland. Half the year there's a lot of snow and ice around. Which I imagine means most of the view is "white" and "shiny". Coupled with the dark winters it's gotta be a nightmare to deal with.

Not necessarily. Depending on angle and water depth, multi-return LIDAR can give you returns from both water surface and the road surface beneath, in the same way multi-return LIDAR can produce returns from vegetation and the ground beneath.

Could you use a different spectrum of EM radiation to detect water? There are parts of the microwave band that attenuate the signal by absorption and I wonder if you could use that. The only clue a human driver has in that situation is in the visible spectrum. The lines of the road disappear from view, which can be challenging to see at night.

If the LIDAR can sense the road close enough to the front of the car, then it could estimate how far underwater the car is.