Depends on where we are in the sunspot cycle, how intense the magnetic storms are, etc.
If we have a really intense magnetic storm, you can see the northern lights in New Mexico or Texas.
Long story short: Yes, you can see auroral activity in Wyoming; you will likely see more auroras in northeast Wyoming than in western WY, and more along the northern border than the southern border. Will you see as many auroras in Wyoming as you would in Alaska? No - Alaska is just so much closer to the polar region that they're going to see the aurora with much lower levels of magnetic storm than it takes to see the aurora in the lower 48.
Here's where you can get a much better idea of what it takes to see an aurora: