Most of the Basin is in USDA Plant Hardiness Zones 4b and 5a. This is the standard used by gardeners and growers to determine which plants are most likely to thrive at a location based on the average annual minimum winter temperature.
The Wyoming State Forestry Division has several good resources for tree owners, including a Tree Owner's Manual and a tree symptom decoder. I have hard copies of the Manual if you would like to stop by the office and pick one up.
The Washakie Conservation District created a Tree and Shrub Guide for Washakie County which is available on their website or in print. They also recommend purchasing trees through the Colorado State Forest Service Seedling Tree Nursery.
The UW Extension Barnyards and Backyards website has a wealth of information on all things related to rural living, including tree care.
Utah State University has a fun Tree Browser website and app.