Chicken wire is not just to keep chickens in, it can be quite effective in keeping many predators out. I don't know what predators you actually have where you are in Iceland, you might chat with animal control on that topic. Many people would be greatly surprised by what animals live in the middle of suburbia other than rats. Here in the States chicken wire will stop skunks, possum, small dogs, certain members of the weasel family, most birds or prey, and many others. Chicken wire, like hardware cloth, comes in different gauges and with different mesh sizes. How effective either one will be depends on the gauge of the wire and the size of the holes. Hardware cloth is normally going to be more effective.
Larger animals like a big dog, coyote, a large raccoon, and others can tear chicken wire or hardware cloth. There are threads on this forum showing pictures of torn hardware cloth, usually torn by big dogs. For either to be torn the animal has to be big enough to have the strength to tear it and has to be able to get a grip. That's another place small mesh comes in, small mesh may make it harder for the animal to get a grip.
One danger point can be around the edges. Excess wire mesh there may make it easier for the animal to get a grip. How well the wire is attached to the frame is important too, your connections may fail. If you don't have a top on the run a flying or climbing predator can get in. You might want to Google "fox climbing fence". You may enjoy watching some of those U-tube videos.
Another thing to watch for is the area around the ground. Many critters only need a tiny gap between the bottom of the wire and the ground to squeeze in. I use the apron method to keep chickens in and critters out.
Many decades ago I spent two years in Denmark outside Copenhagen. If your style of building is similar I can see why you are pretty comfortable ground based predators that can't climb aren't much danger. In suburbia dogs are probably your largest danger.
A story. We had a member of this forum years ago that was a certified poultry judge that raised and showed chickens. For decades his breeding pens were made from chicken wire and he had no problems. Then one day while he was away two large dogs found his chickens. His wife, who just the day before had come home from serious surgery, took the shotgun out to try to stop it but those dogs wiped out his breeding stock. His wife was not seriously injured doing that but he was really worried about her. And he was so heart-broken he wasn't sure he was going to start again with his breeding program.
The moral of the story is that your protection works until it doesn't. You never know until it is tested and if it works you may never know it was tested.
Some people can free range and not lose a chicken to a predator for years. Others would be wiped out as soon as they tried. A minimal coop may be all you need. We all have different risk tolerances and different predator pressures. As long as you build wisely, the more you spend the safer your chickens can be. I don't know what level of protection is right for you.
