Under the Wilderness Act of 1964
domestic livestock grazing is specifically allowed in Wilderness.
Furthermore, in the late 70's, Congress released House Report 96-1126 stating : "To clarify any lingering doubts, the committee wishes to stress that this language means that there shall be no curtailment of grazing permits or privileges in an area simply because it is designated as Wilderness."
Congress released very specific instructions to allow grazing to continue in Wilderness Areas. In 1990, House Report 101-405 (commonly known as the Congressional Grazing Guidelines) states: "There shall be no curtailment of grazing in wilderness areas simply because an area is, or has been designated as Wilderness, nor should Wilderness designation be used an excuse by administrators to slowly 'phase out' grazing."
Maintenance and replacement of grazing facilities - such as fences, water wells, and stock tanks - is permitted in Wilderness. The use of motorized vehicles needed for temporary and occasional maintenance or emergency purposes is also permitted.
Sky Island Alliance has been actively engaged with Tumacacori Highlands ranchers, Coronado National Forest officials and Sky Island Alliance's partners to make the Tumacacori Highlands Wilderness proposal the best it can be.

Wilderness Generally Increases Stock Allotments
In a 1991 study published in the Journal of Range Management, Mitchell P. McClaran of the University of Arizona found that Wilderness designation on the Coronado and Tonto National Forests did not initiate grazing use reductions by the U.S. Forest Service. In fact, the study showed that there was a general increase in stocking of allotments in wilderness relative to non-wilderness allotments in the forests (McClaran 1991).
McClaran, Mitchell. "Forest Service and livestock permittee behavior in relation to wilderness designation," Journal of Range Management , 44 (5) September 1991.