I have used dedicated snow/ice tires.... yes always all 4.... for the last 30 years on our commuter car. Dunlops, Michelins, Yokohama, and a couple of other brands.
I usually put them on around Thanksgiving, but have occasionally put it off until snow arrives, around Christmas, and remove them by April 1.
With a 70 mile round trip commute, they have all lasted 5 or more years - still greatly outperforming all-seasons at that time.
They are all so hugely superior to any all-season tire that I am sure you will love the Michelin Xi-2 tires... and yes we just put some of those on our Corolla.
To the poster that suggested putting them on the front only: If you do so, please limit your top speed - in snow - to 20mph, and do not drive on any roads that I am on!!
Take a grocery cart and push it backwards for a while (caster wheels on the back now) and you can simulate this wild ride!