1.) Every thing I'm about to type ismy opionion and interpretation. I'm not a lawyer nor am I a Law Enforcement Officer. You should research statutes and if you feel the need, call the Sheriff's office of the town your going to (though they dont always know the laws all that great). But, I live in Wy and carry every day, every where, all the time. This is my experience.
2.) What part of Wyoming are you going to be in??
3.) Well, you pretty much answered your own question. Wyoming has NO laws against open carry. If your weapon is not concealed than you can carry openly. There is no law about how much needs to be shown. If you can see the weapon then its not concealed. BUT, I would be smart about it. IWB with a tucked in shirt will probablybe fine. OWB is probably better. I carry all the time OWB. I have never had anyone say anything to me about it, except for friends asking me about what kind of pistol I have.
Wyoming is a very gun friendly state. If your smart and respectful then chances are very good that nothing will happen. If it does, well, thats just bad luck. I know my answer was kinda vague, but its really the only answer. Hope your have a fun and safe trip!!