With the necessary proviso that "Native Americans" applies to literally millions of people that occupied two continents for ~18,000 years, I am willing to take a shot at this from the perspective of the southern Northwest Coast Cultural Area. Tribes in Northern California and Southern Oregon made use of trails in a variety of terrains including and very frequently in hilly or mountainous terrain. In fact, some major ridge systems of the interior mountains were used for north-south travel and trade starting around 6,000 years ago and continuing into the historic period.
Indian trails required very little maintenance. They were seldom more than a lane through the forest or prairie, with perhaps an occasional log across a creek. Of interest to anthropologists is that trails were the subject of a variety of very stringent cultural norms and customs. Among tribes like the Wiyot, Yurok, Hupa and others, trails, like people and animals, were sentient. And they were, like many creatures, related to humans. They were afforded consideration and the rules about them were followed lest one be affected by bad luck or, perhaps worse, considered ignorant or low class.
There were women's trails, men's trails and trails for both. There were trails used only by the high status individuals often associated with routes taken between dance sites. There were trails to peaks in excess of 6,000 feet elevation, used only by doctors, students preparing to be doctors and people accessing holy areas for spiritual renewal, pursuing vision quests, and praying for good fortune and wealth. There were trails only for menstruating women, pregnant women and for women for a stipulated period following childbirth. And there were stories of very special trails that old people took to sacred sites in the mountains and came back young again.
Some of the customs that applied include the requirement to throw sticks and/or rocks on piles adjacent to the trails "for luck" (this custom continues to be used today), using only specific resting or stopping areas so that you do not insult the trails, and prohibitions of use by certain sex, status or other category of people.
Common trails, often being on ridge tops, or along streams frequently corresponded with dividing lines between tribe/nation/group territorial boundaries. They were, like rivers, areas that could be used no matter what tribal affiliation the users had. Travel was recognized as something everyone had to do. This certainly did not apply if your people were at war with other people in the area of the trails and it did not apply to trails about which customs dictated special use, like those specifically for women, high status people or doctors, for example.
In short, trails like virtually every other aspect of these rich cultures were part of very complex belief systems that dictated their treatment and consideration.
There has been quite a lot published on this subject so I am providing you a bit of a reading list. Many of these can be found on line.
Mavis McCovey, John F. Salter 2009. Medicine Trails: A Life in Many Worlds Heyday Books
John Peabody Harrington Linguistic and Ethnological notes on the Chimariko and Hupa
P. E. Goddard 1904. Life and Culture of the Hupa, University of Californa
Thomas Buckley 2002. Standing Ground: Yurok Indian Spirituality 1850-1990
Richard Keeling 1993. Cry for Luck: Sacred Song and Speech Among the Yurok, Hupa, and Karok Indians of Northwestern California
Lucy Thompson, Julian Lang (Introduction), Peter Palmquist (Introduction) 1916. To the American Indian: Reminiscences of a Yurok Woman
Thomas M Gates 1995. Along the ridgelines : a history of the Yurok trail systems. Ph.D. Dissertation Univ. of North Carolina, Chapel Hill
Edit: Typos and grammar