BLM rules and regulations for Wilderness Areas are codified under…
§ 6304.25 What special provisions apply to livestock grazing?
(a) If you hold a BLM grazing permit or grazing lease for land within a wilderness area, you may continue to graze your livestock provided that you or your predecessors began such use under a permit or lease before Congress established the wilderness area.
(b) Your grazing activities within wilderness areas, including the construction, use, and maintenance of livestock management improvements, must comply with the livestock grazing regulations in part 4100 of this chapter.
(c) If the management plan for the area allows, you may maintain or reconstruct grazing support facilities that existed before designation of the wilderness area. BLM will not authorize new support facilities for the purpose of increasing your number of livestock. The construction of new livestock management facilities must be for the purposes of protection and improved management of wilderness resources.
(d) BLM may authorize an increase in livestock numbers only if you demonstrate that the additional use will not have an adverse impact on wilderness values.