As a veteran of many trips back to the Big Horn area, I have to agree with Dave. 4WD is not required though, as Steve later mentions, if it rains more than a bit, the game changes. What is helpful is a reasonable amount of ground clearance, and a degree of caution. The less ground clearance your vehicle has, the more caution required, but I regularly see basic sedan type vehicles back in the Big Horn area.
I have to admit to some mixed feelings about detailed maps and all of that, however. During my first forays in to explore the eastern side these many years ago, the lack of specific information was very much a part of the fun and adventure. I'm kinda glad that railfan specific maps, the internet and all of that weren't around then, as I got to discover things on my own with the help of a few topos & FS maps augmented by a few educated guesses.
Following in the very detailed and well-described tracks of others does spoil the adventure a bit, don't you think?
Scott