Full winters on steel rims is my recommendation and what I use.
A winter tyre is not only about the tread pattern, it's about the rubber compound being soft enough to grip the cold road. Switchover time is 7 Centigrade, and with them on rims it is easy enough to do it yourself. Note that tyres are not designed to be mounted and unmounted multiple times, so just get a set of steel rims and anyway it will cost you less than swapping the tyres on and off the rims in the long run.
I currently have Michelin X-Ice 3, but I'm not that impressed with them. Recommendations that I've seen from other people are Bridgestone Blizzaks or Nokian Hakkapeliittas.
I will never cheap out on tyres. They are the only things in contact with the road, so the only things letting you brake and steer away from an accident. The EV torque also means that you need good grip to maintain control.