Iceland is not entirely ice covered all year long, but the weather is variable to say the lease. Based on personal experience and the warnings given in every guide book I've seen, do not begin a hike or a drive in remote places if the weather is the least bit questionable.
Iceland is an island in the middle of the North Atlantic ocean. Although it is a large island, it is strongly affected by weather changes that come by sea. The Internet has improved the ability of weather forcasters to get the latest word out to even very remote areas of Iceland, but it is no joke that the weather broadcasts are some of the longest in the world.
Incredible banks of fog can roll in. Apparently clear skies can turn rainy. Rain to sleet and sleet to snow very quickly. Never leave your shelter on foot or even by car without taking along a jacket, high energy foods, water and a radio. If you are on the 'right' side of the mountain, the radio might even work.
You can have avalanches, rock slides, volcanos, violent storms and many other situations that will convince you that you are not in Florida. From our Alaska experiences, we always have jackets with pockets full of gloves, hats, candy bars, matches, a first aid kit and much more. This gives us the appearance of being penguin-shaped. I'm not ashamed to admit this, but I do feel better prepared for circumstances.
We did carry detailed maps, but often without roads or the presence of other obvious landmarks, they were much help. After a while one mountain starts to look amazingly like another. You wonder if you are on a trail meant for people or one left behind by animals. Then, when you least expect it, the trail peters out......what next?
Be smart, be safe, be careful!