There is no need to be worried about visiting Iceland in the winter; as long as you are flexible with your plans and check the weather forecast.
The average winter temperature in Iceland is just about freezing 20-35*F [0 to -5C] and while it can get colder and warmer in general the temperature hovers around the freezing mark.
The days then tend to get longer from there, gradually up until March where the days tend to be longer than the rest of Europe.
Not all roads are cleared and there could be black ice patches so take it easy. It can be tempting to speed as the roads are often clear but don’t; it’s illegal and dangerous.
Iceland is one of the most expensive countries in the world so visiting Iceland in winter means you are going at the cheapest time.
The best investment for your Icelandic winter trip is a waterproof and windproof jacket, waterproof trousers, and waterproof snow boots.