My first thoughts were when you said the three words Wyoming, summer, and coat, where exactly will you be, and what month will you be here? Most of the state can be in the 90's to over 100 degrees in summer, unless you are pretty high elevation wise. Wearing a coat may not be practical. And, depending on what you're doing, why conceal it? Out of town is not going to raise any eyebrows to OC unless in a National Park, in town, crime is about as nonexistant as you can imagne.
As has been mentioned, a shorter gun, or cutting yours down, may be more practical than carrying the long one.