While I suspect you are thinking in terms of the trade in beaver pelts and deer hides, Pueblo people in the Southwest highly valued bison hides beyond their utilitarian value as winter material.
There was extensive trade between Pueblo groups in New Mexico and nomadic groups in the southern Plains and the Four Corners region. This is documented historically in terms of trade fairs (for instance, famously, at Pecos Pueblo - a gateway between the Plains and the Rio Grande drainage), but archaeological evidence (significant Pueblo artifacts found well into Texas and other parts of the southern Plains) and the existence of these trade fairs at the point of European contact suggests they have some antiquity in pre-Hispanic New Mexico (probably as far back as the 14th century A.D.) (Spielmann 1983).
While bison meat was a valuable trade good because of over-hunting of large game in the environments closest to the large, aggregated Pueblo villages of New Mexico, the hides were a large factor in the trade with the Plains. The hides very likely had a utilitarian function, with Spanish accounts indicating men at Hopi used bison hides for warmth in the winter in the 16th and 17th century (Graves 2004: 50).
However, the hides also had social significance beyond their use as winter clothing. Bison (including horns, not just the hide) is a common component of ritual paraphernalia in Eastern Pueblos (those along the Rio Grande) in the 20th century, documented ethnographically by early anthropologists, including at San Ildefonso and Santa Clara Pueblos (Graves 2004: 50). The hide could be worn as part of a headdress (perhaps along with horns), or on arms and legs. Bison-hide robes are another ceremonial item attested in 20th century Pueblo rituals.
While the archaeological evidence for this significance of bison hides is less robust, there is good reason to believe that the well-documented trade in bison hides between southern Plains and the Pueblos was driven at least in part by the ritual significance of bison hides (and other parts). For instance, a bison-skull mask was found in a kiva (a religious structure) at the Pueblo of Gran Quivira dating to around A.D.1500 (Graves 2004: 50). Importantly, Gran Quivira is part of a cluster of Pueblos on the eastern side of the Rio Grande Rift, with easy access to the Plains groups trading in bison hide. Likewise, historic Spanish accounts from the 16th and 17th century mention the importance of the bison hide trade, including the importance of trade in bison hide robes already mentioned as ritually significant objects in 20th century ethnographic accounts (Creel 1991).
In summary, bison hides (and other bison products) where valued (and continue to be valued) by Pueblo people, beginning at least by A.D.1400. Bison were valued not only as a source of meat and warm furs, but also for their use as part of ritual paraphernalia (especially the hides as parts of headdresses or in robes).
Sources
Creel, Darrel. 1991. Bison Hides in Late Prehistoric Exchange in the Southern Plains. American Antiquity, 56(1):40-49.
Graves, William M. 2004. Social Identity and the Internal Organization of the Jumanos Pueblos Settlement Cluster in the Salinas District, Central New Mexico. In The Protohistoric Pueblo World A.D. 1275-1600, edited by E. Charles Adams and Andrew I. Duff. University of Arizona Press.
Spielmann, Katherine A. 1983. Late Prehistoric Exchange Between the Southwest and Southern Plains. Plains Anthropologist, 102(1):257-272.
We do not know a lot about the importance of hides in the northwest prior to contact. Since hides do not preserve at all in wet climates, we have no archaeological data on prehistoric hide use. We can infer that certain hides were valued by looking at the ethnohistoric records. Mink, otter, elk goats and sheep and a variety of pinnipeds (sea mammals) figure prominently in the ethnohistory of the Northwest Coast. Mink, weasel especially in the winter phase (ermine), wolf, otter and bear hides were employed in dances and other rituals. Buffalo hides were traded for salmon at the annual trade fair at The Dalles, Oregon. Other hide use, which appears to make up the majority of hide use was strictly utilitarian, used as bedding, robes, or other household uses.
Native relationships with fur bearing animals changed dramatically with the onset of fur trading in the late 1700s. Natives became very adept at trapping and shooting desirable furbearers as their economy began to revolve around trade from about 1800 on. This subject is quite a ways out of my lane, so I hesitate to say more.
Sources:
K. Ames and H. Maschner, Peoples of the Northwest Coast, their Archaeology and Prehistory. 1999, Thames and Hudson. London.
R.G. Matson and G. Coupland, The Prehistory of the Northwest Coast, 1995. Academic Press, London
Lee Lyman, Prehistory of the Oregon Coast, 1991, Academic Press
Handbook of North American Indians, vol. 7, Northwest Coast, 1990, Smithsonian
This Site has some interesting information. Note the photos of shaman using bear - hide robes during healing.