Yesterday in light rain, I got the "Cruise Unavailable" message which it explicitly blamed on poor front camera visibility. It was night and it was definitely hard to see the lane markings on the wet pavement, but then I wasn't try to engage autopilot. It was no problem at all to see the cars ahead and I can't image the radar would have a problem tracking them. Elon has said he doesn't like LIDAR because it isn't all-weather capable whereas radar can be mostly immune to rain and snow.
The curious thing is that it turned on once, in the same conditions and was fine until I manually turned it off, whereupon it refused to turn back on for the rest of my drive. I was making a quick shopping trip, so when I got back in to drive home in the same conditions, the first try it turned on and worked fine until I turned it off manually, after which it refused to come on again all the way home.
The dash would occasionally show the lane markings on the road, but not the cars in front of me which were much easier to see than the lane markings.
I've previously used TACC in much worse rain with no problems at all.