Snow tires or studded tires are practically necessary when there's snow on the roads. On very bad days, only fatbike-width snow tires or studded tires work. On the very worst days, even those won't work and you have to resort to walking or to a car.
Studded tires are necessary on ice -- the smoother the ice and the higher the temperature of the ice (more close to melting point), the more necessary studs are. If you live in an area where roads are icy only occasionally, you may be able to just avoid riding on those icy days, or if ice is only very rare, by riding carefully on the ice and riding less carefully on pavement. However, there are plenty of people in areas where icy days are prevalent and who would miss riding a lot during those icy days.
Thick tires, such as studded or snow tires, perhaps even with a puncture protection armor such as Tannus armor, are necessary when the roads are covered with gravel intending to prevent pedestrians from falling on slippery ice.
Since most people won't want four kinds of tires (road tires, studded tires, snow tires, thick armor-protected gravel tires) and since some of those requirements may overlap (for example if riding on ice that has gravel distributed over it, you may need both studded tires and thick armor-protected gravel tires at the same time, and if riding on paths where both snow and ice occur, you may need both studded tires and snow tires), the best course of action is to choose a studded tire that works equally well on snow due to its tread pattern and put a puncture protection armor such as Tannus armor in it to prevent sharp gravel from puncturing the tire.
May car drivers use stud-free winter tires because cars tend to grind the pavement to dust, causing air pollution and health problems for sensitive people. However, this only works if some small percentage (at least 10% or so) of drivers choose studded tires because the studded tires make ice less smooth, increasing traction for stud-free winter tire users. Also cars do not depend on traction for stability due to having four wheels, and also cars are heavy so studded tires cause lots of pollution and pavement wear whereas bikes are lightweight and thus studded bike tires cause very little pollution and pavement wear. Due to these reasons, even if 90% of car users can get away with stud-free winter tires, you shouldn't do the same on a bicycle: you should use studded tires.