Hello, 1st post. Car knowledge level: expert, although I know nothing about Tesla I'm interested.
A few things nobody mentioned: 245 width tires are moderate to narrow for a 4600 lb car of this performance. Wide tires do skate over water/rain much more easily than narrow tires but I don't think this is hydroplaning because the tires aren't terribly wide and the car is pretty balanced. Are you losing traction with the road? No idea, I've never driven a Tesla.
Ice pedal: I've had it twice and heard of it happening a few times to other people and it's not fun. I don't know the specifics of the Tesla system so I'm not speaking of the Tesla specifically, only cars in general. This usually happens when the ABS system gets confused and takes away the brakes. It's happened to me when I'm driving too fast on the street and I hit a pothole when braking. I've heard of it happening on the track when someone bumps a curb or the car is unloaded in a strange way. It's a known issue with Porsche and BMW that see the racetrack (and probably many other cars that don't see racetracks). On the track, unless you're running for money or your career as a pro, it's a good idea to pump the brakes before entering a hard brake because you want to be sure they're there, the pads can lose contact with the rotor for a number of reasons previously discussed, and slow in-fast out. It's not as fast but it's faster than a crashed car
Normal ABS operation: I've had the ABS kick on normally on ice, it takes away all braking authority because ABS is NOT a braking aid, it's a steering aid. It actually hurts braking under most conditions. Perhaps the ABS system is tuned too sensitive. You should feel the ABS pumping the brake pedal but I don't know about the Tesla since I don't know the systems on this car.
If you ever lose braking authority, a good idea is to completely release the brake and reapply them. Opposite of what your natural reaction is, to press harder and lock your elbows for the brace
In any case, people in general follow way too close, especially in the rain and snow. Slow the F down.