In case you have not noticed private land often preclude or complicates access to Idaho peaks. The Owyhee Mountains and West Mountains and most of the mountain ranges in southeastern Idaho are interspersed with private land. While these ranges are the most likely to have access blocked by private property, you may run into access issues any place you go.
Margo Mandella wrote an article summarizing the law and its implications. The article does not offer legal advice but it should help you understand the legal status of private property in Idaho and the consequences of trespassing. Read the article at this link: Private Property, the Idaho Code, Trespassing and You by Margo Mandella