The Rocky Mountain based trappers used a variety of shelters, from none at at all, to small cabins for extended winter camps. If conditions were even somewhat favorable it is likely that no shelter was constructed, or perhaps a simple blanket or tarp was hung over a cross pole or rope to provide overhead protection. Sometimes more elaborate shelters were necessary. Below you'll see some illustrations and descriptions of some shelters that mountaineers used. The illustrations are courtesy of Rex Norman.
One of the more common tents shown in Alfred Jacob Miller's paintings of the rendezvous, is this type of A-Frame or Wedge Tent. These are very simple to set up and can also be opened up into a lean-to if there are doors on both ends.
This type of shelter is reminiscent of the Indian Tipi. It is constructed with a simple tripod foundation and additional poles set in place. Then the frame work is covered with ground cloths or tarps or pack mantees and the loose ends secured. Be sure to stake down the edges of the tarps, or securely stake a rope around the top of the framework and down inside the shelter to provide stability in a wind.
This shelter is known as a "Quarter Sphere" or a "Half Dome." Construct it by planting fresh cut willows firmy in the ground in a half circle and bending them over and securing them at the top. Lash horizontal saplings on and cover the frame with the same tarps or canvas. Again, be sure to anchor this well to the ground so it doesn't blow away.