I've found looking in Google Street Map that in Iceland sometimes you find gates in public roads like this. In my country (Spain) these are very rare, but when they exist is because there are free cattle or something similar and you can open, enter and close the door if it's closed. In Iceland it's the same? Or they are used to close forbidden roads? (i.e. because there is too much snow and is impassable).
I think you are misreading the picture.
There is a grate running across the road itself that cars can cross without problems but hoofed animals (e.g. sheep) can not. Next to the road there is a gate that can be opened when driving herds. But this gate is never used to close off the road.
Generally, in Iceland, a closed gate means no entry. Unless there is a sign stating otherwise, I wouldn't presume to go through any closed gates.