Just out of curiosity, how many people here have visited Wyoming?
My mom is from Wyoming and practically her whole family lives there. So I'm there every few years visiting them/just road tripping, and I get to talk politics with them a lot. Some would say too much.
I think the two main things to understand Wyoming's politics are the high amounts of irreligiosity and the extremely high levels of small business ownership + self employment. The largest non-government employer in the state (Rio Tinto Energy America) has just 1,795 employees. If you ask people the top issues that they vote on, I'm guessing the top three are guns, cutting red tape, and hostility to coal and oil. Obviously, the Republicans are going to have the edge on those issues.
At the same time, religious conservatism and race-baiting aren't going to get you as far in Wyoming as they might in other strongly Republican states. I think Ted Cruz did well in the caucus because he probably had the best-organized campaign at the time, which is needed to win in a very rural caucus state. But I really don't think he would be the top choice of most Wyomingites. I think most would fall somewhere in a spectrum between Rick Perry and Ron Paul.