LOL! I've answered that question so many times I should frame it.
There is no statute or other word about open carry anywhere in the Wyoming law. It's just not mentioned.
There ARE federal laws that apply to the people of Wyoming, but are not listed in the Wyoming law.
Wyoming has complete preemption, which means that nobody but the state of Wyoming can make laws regarding gun use, carrying, etc. Some cities have old statutes on their books that predate the preemption, but they are null and void. Some cities try to intimidate people with them even now, but they will back down fast when presented with the facts. There is a thread here somewhere about Pine Bluffs and a recent incident where someone was threatened with arrest over open carry.
The owners of private property can prohibit guns in any form they wish. I have not seen any businesses so posted here, but there might be in some of the larger cities. If the business isn't posted, and an owner or manager asks you to leave, it is best to just do so. I have a card that I would hand out to such a business.
You have forbidden me to carry my self defense tool into your store. I am going to respect your wishes, but I want you to know that you have lost my business now and in the future, as long as my sidearm is not welcome. I will also inform my friends of your policy.
Self defense is a natural human right.
Second Amendment Sisters
So far I've handed out dozens as samples, but never had to use one for a business.