I think most people here stick to talking about handguns because they're the more convenient option for self-defense, but that's not to say we haven't talked longarms before: http://opencarry.mywowbb.com/forum20/2184.html is a long tale mentioning the man's younger brother who carries a .22LR rifle as he's under the age of 18 and can't carry a pistol yet. In terms of legality, most of the difficulty with going armed with a handgun isn't a problem with a rifle or shotgun, so long as it's carried openly. Texas, for example, requires you to have a CHP and carried concealed under most circumstances in public... yet if you have a rifle, it's likewise a crime if you don't carry it openly.
I double-checked the AG's website for Wyoming, and WY issues concealed handgun permits rather than concealed weapon permits; if you wanted to carry a longarm up there, that'd be a good strong basis for any official LEO contact to state that you MUST carry it openly, and that any suggestion they might make otherwise constitutes a request to commit an illegal act. And in Wyoming, aside from the "urban" centers of Laramie or Cheyenne, I doubt many folks would be alarmed by someone carrying a rifle down the street (although it may be odd and get you questions from time to time). Beyond that, the only limiting factor for me would be convenience... how to set it aside while eating at a restaurant and that sort of thing.