If the mining claim is "patented" it has been bought from the govt., and is private property. Otherwise, a mining claim only gives either the surface or below surface mineral rights to that piece of ground, depending on the type of claim (placer or lode). While the claim holder can't legally keep you from crossing the claim, the agency involved usually works with the claim holders to minimize vandalism theft, and chance of injury. You should get a list of claim holders in the area you would like to use, and get with them and the agency to explain who and what you are, and what you would like.
1981 Cherokee W/T, 360, T-18, Warn 8274 in custom bumper/deer strainer (tested and approved)
1988 Cherokee 4 door, 3" Rancho lift, custom sliders/steps, custom roof rack, custom camo paint, custom camo headliner, custom bumpers and Warn 9500 HS, 31-10.50's
Only 31's, but can drag self with either rig
BLM John Day/Snake RAC-OHV/Recreatrion Representative
Wolfpack 4x4's - Region 5 - "Cave Lupum"
VP- Outcast Land Use Review Team