This is a complicated topic. I used to own the lower part of a mountain valley (out west but not in Montana). There were two dirt "roads" into the valley, both immediately against the titled property; the rest of the valley was Federal (BLM) land encircled by mountains that were effectively impassable. Americans generally have a right to use and temporarily occupy these Federal lands without permission, so if I put up a gate/sign it would effectively be like owning the entire valley.
There are three big issues when you own land like this that people overlook, both of which can be described as "tragedy of a pseudo-commons":
- The Federal government likes to use these roads across private and public land but not only doesn't do maintenance but enforces a stack of regulations that actively prohibits others from doing repairs to damage caused by their traffic. Filling in a pothole requires environmental impact studies, archaeological assessments, thousands of dollars in fees, etc. The nice dirt roads you find up in ranch country in Federal wilderness areas are often maintained illegally by locals because the government won't do it and the cost of doing it legally is completely unjustifiable. For some people, it is easier to just disallow road access.
- Most ranchers do not own the mineral rights of the land, and mineral rights come with privileges that allow mineral exploration companies to abuse your land for the purpose of mineral extraction with little recourse. An effective strategy to prevent this is to actively prohibit the mineral exploration companies from trespassing to establish that there is mineral worth extracting. I've dealt with this twice. Among other things, it requires aggressive enforcement of a "no trespassing" policy that mineral companies will try to ignore or subvert.
- People thinking that the private land is Federal and acting under those assumptions, including vandalizing, stealing from, and generally trashing things as Federal agencies do very little to police this. Unfortunately, this is a really common problem in wilderness areas. They tend to avoid areas that look like they are actively managed lest a rancher show up -- well-maintained signs and gates are a good proxy.
How this plays out in practice when these issues become a big enough problem that the ranchers start putting up signs and gates everywhere, with the common understanding that these are not for the locals.
After years dealing with the above issues, we eventually did like everyone else and prohibited use of the roads (except for locals of course). I would say it was only marginally effective but it was better than the previous situation.