In Wyoming, you will find lots of places you can boondock, however, you will probably want to drop the trailer if you are wanting to explore along some of the remote sections which can only be seen from dirt roads. I think it would be a hoot to follow the route as close as possible.
If you do travel any of the dirt roads and get caught by a sudden rain storm, I suggest you immediately stop and then wait for about 1 hour after the rain stops before trying to go.
We were just west of Casper exploring a section of the Oregon trail when we had a rainstorm hit. The road immediately went slick. I had to get out and engage the front hubs and almost fell down a couple of times. We did manage to drive the 1/2 mile out but came close to sliding off the road a few times and wouldn't have made it if the we had to climb a hill. My father made a comment that he would rather be driving on ice as it had more traction.
Just a warning to be careful and always have water and food with you just in case.