The Soil Conservation Service of Iceland (SCSI) is actually working *with* a number of sheep farmers on revegetation – the project is called “Farmers Heal the Land”. Furthermore, a new bill on soil conservation was passed late last year (December 2018). The Icelandic government is going to put 30.000.000 $ into carbon capture projects in the next 4 years including reforestation and soil conservation. I don´t think grazing livestock is going to be an issue – that´s what fences are for.
I´m unusually optimistic about this.