First car, hmm? Congrats on a fine choice
Ice is about the worst road conditions possible. Very dangerous. All-season tires are barely passable (at best) in snow, and of nearly no value in ice. Low rolling resistance tires make the tires even worse in cold, icy conditions. If you drive in theses conditions much at all, you *must* get winter tires.
Many people that get winter tires get a spare set of wheels to go along with them. That way, the costs of swapping out tires (and rebalancing) twice a year are gone, and so is the extra wear-n-tear on the wheels (from the salted roads, from the moisture, and from the scrapes of the tire-changing machines and their operators).
I'm fortunate in that I see ice and snow about two days a year (one was today, although no issues at all - just a light snow-dusting). If I lived much further north, though, I'd have a winter set of tires and wheels.