First, in a car without ABS, I put on the brakes (I was probably going a little too fast) to avoid hitting the car stopped ahead of me. I started to slow down, but also to slip to the right towards the curb; it was scary, and I barely slowed down in time to avoid either collision.
Second, in a car with ABS, I slowed down to turn into a parking lot, and the ABS kicked in; the car went absolutely straight (without slowing down enough to make the turn), but I wasn't sliding at all, so I didn't have to worry about sliding into the curb. Big win.
Instead, it's all too happy to drift into oncoming traffic at a glacial pace. It could be specific to the various Toyotas I have owned...
Sorry to hear you had that experience! I've lived places where the "sink into the snow" was the right thing, but where I live now, there's very likely ice under the snow, so it's not clear if that would help.