It is forbidden to drive motorized vehicles off-road in Iceland.
However, it is permitted to drive such equipment on glaciers and frozen/snow-covered ground off road outside urban areas, if the ground is frozen or the snow cover is solid, and it is obvious that there is no risk of damage to the surrounding nature.
It is allowed to park a motorized vehicle one car's width away from the road if it does not cause damage to the nature or create a risk of accidents, although this is in accordance with the provisions of the Traffic Act and the instructions from the Icelandic Road and Coastal Administration.
More information regarding off-road driving can be found
here.