My 2014 Prius has terrible traction on snow and ice. Worst than other front wheel drive cars, and worse than most of rear wheel drive cars I have driven. I think it is due to 2 things: 1) The low rolling resistance tires were not designed for snow or ice. 2) Virtually all of the braking is done with the front wheels. The rear brakes are used only below 7 MPH and during emergency stops. Have other Prius (or hybrid) owners improved winter traction with different tires?
I don’t own a Prius myself, but this is probably going to be your biggest culprit. Low rolling resistance trade poor weather traction for better gas mileage. I would recommend purchasing a set of steel wheels and having winter tires mounted onto them so you can switch from your all season tires to the winter tires when you need to every winter.