Over the winter I had the opportunity to take our Model Y (LR) onto a frozen lake. Let me tell you the Model Y is about the most boring car in the world on a sheet of ice. It WILL move but it will not hang the tail out, if anything it understeers or if there is any grip to be found it just turns as you'd expect, but usually with more understeer than normal. I've previously been on the same lake in my old RWD Porsche 996 and various Audi Quattros and a Jeep Wrangler, all of which were a total blast, usually with Blizzaks or the like, but nothing studded. But not the Y, it was boring. The aim was to figure out what it would actually do in a low-traction situation, I definitely got my answer...so it was worthwhile.
It has so much software just stopping and controlling its dynamics that I don't think you'd ever need to be concerned on any normal road, no matter the conditions unless you floor it and purposely steer towards a tree or a crowd in which case it will almost assuredly get there faster than you anticipate. When on ice there are two modes (Off-Road mode and Slip Start mode) that can be selected from the car settings screen (scroll down a bit). OffRoad locks the torque split 50/50 which gets you going and does help in cornering on the ice, and Slip Start lets the wheels rotate and spin somewhat rather than the traction control clamping on the brakes, just enough to keep going.
Tires were Vredestein Wintrac Pro, a semi-performance winter tire that was excellent in the ice and snow of the Colorado roads this winter.