Because I live in a sub-tropical area, so , I really need your help with this question.
When you said:
"It's still raining, even though it's getting colder, which means it'll probably turn to ice." and "ice storm"
does "ice" here mean snow? or something like hail?
It is probably meant that the rain will turn into freezing rain. In the winter the air may be above freezing, but the ground may be colder. So rain falls to the ground and freezes into ice where it falls. When this happens the entire world, cars, trees, buildings can be coated with layers of ice.
Rain that begins to freeze on the way down is called "sleet."
"Hail" is actually more of a freak summer type occurrence. Balls of ice may fall during certain conditions in certain thunderstorms.
An ice storm is very bad news if you need to go anywhere. Snow can be plowed out of the way, and tires can find traction in snow. Not true for ice.