The Secretary of the Interior shall permit, under regulations to be prescribed by him, the free grazing within such districts of livestock kept for domestic purposes; and provided that so far as authorized by existing law or laws hereinafter enacted, nothing contained in this subchapter shall prevent the use of timber, stone, gravel, clay, coal, and other deposits by miners, prospectors for mineral, bona fide settlers and residents, for firewood, fencing, buildings, mining, prospecting, and domestic purposes within areas subject to the provisions of this subchapter.