I ride a lot in the rain here, but had the misfortune to get into a heavy wet snow once. I completely lost rim braking. The tracks became ice covered and were so slick that the brakes couldn't generate enough friction to melt it in a reasonable amount of distance, say a hundred feet. That was not good. It was a group ride. Some people used the Flintstone put-your-feet-down method. Conditions like that are rare, but they do occur. Also the cassettes iced up so that we had single-speed bikes. Only the cog in use wasn't covered in ice. Peeing on your bike in public is kinda weird.
The other thing is that they sand the roads here, so when the snow is gone the sand remains. I wear out about a rim/year. Cost isn't too bad because I build my own wheels, but discs are rather attractive for that reason alone.