In my locale, the "other" winter hazard is road salt. They lay it down thick. So I have a dedicated winter bike with studded tires, and I bring it out when the salt trucks come out. Then I put it away again in the spring when the heavy rain washes the salt away. Actually what they spread on the roads is a mixture of salt and sand, so it makes a mess of bikes. Switching tires back and forth during the winter gets old, since my garage is only semi-heated.
The winter bike is on a Schwinn Varsity frame. That'll take a while to rust through.
Some riders in my area use a studded tire just in the front. This will handle most of the cases where you hit an isolated ice patch and just want to maintain control. There's also less rolling resistance from the front tire. It won't be enough for those ice storms where everything is covered with 1/2 inch of sheet ice, but those are pretty rare. There have been days when the only people who made it to my workplace at all were the cyclists.
And what I've noticed is that some cyclists simply live without studs and make their way as best they can. This may involve walking the bike from time to time.