The answer to the question of whether or not an airport can be shut down by the Wyoming variety of wind is actually, "No." The First expert asked was someone I've known all my life, my oldest brother, Mike. Anytime I ever got him talking about flying, I always got more than I wanted to know. (But he always makes what I learn really interesting.) The second (real) expert who confirmed Mike was right is Cheyenne Regional's Operations Manager, Gretchen Eichstadt:

The airport actually never closes due to wind, but each aircraft has wind limitations. It's up to the pilots to check conditions and determine whether or not the winds are within safe operating limits.

The only place in Wyoming to truly get away from wind might be a missile silo, or a bomb shelter at a friend's old house. At the airport of Wyoming’s biggest town, however, whether or not an aircraft can take off depends.

Non-safe take offs are rare for an airport that is civil and military, like in Cheyenne, with mighty C-130s. Bro also mentioned another example of danger in the wind - landing:

But in a B-52, you just 'dial in' the degree needed and the gear turns to maintain the 'crab' all through touchdown.