This is the only Wyoming law regarding carrying that I could find:
6-8-104. Wearing or carrying concealed weapons; penalties; exceptions; permits.
(a) A person who wears or carries a concealed deadly weapon is guilty of a misdemeanor punishable by a fine of not more than seven hundred fifty dollars ($750.00), imprisonment in the county jail for not more than six (6) months, or both, unless:
(i) The person is a peace officer;
(ii) The person possesses a permit under this section; or
(iii) The person holds a valid permit authorizing him to carry a concealed firearm authorized and issued by a governmental agency or entity in another state that recognizes Wyoming permits, is a valid statewide permit, and the state has laws similar to the provisions of this section, as determined by the attorney general, including a proper background check of the permit holder.
The map on the home page says open carry is allowed in a vehicle, but the gun must be visible, which would correspond to the law above. The only thing illegal is concealment, loaded carrying is not illegal. However, it has been noted that Wyoming's preemption statute is shaky and I don't know if there are city/county ordinances that would affect OC and vehicle carry.
I am almost ashamed to claim Wyoming as my home state now.