I am going to try do some felted slippers in Plötulopi next time.
But now I at least know that it is possible to felt Icelandic yarn. However, I had to wash the pieces twice in 60 degrees Celsius in the washing machine.
This is how the pieces looked like when I had knitted them:
And this is how they looked like after sewin them together:
And this is the result after washing them twice in the washing machine: