In October we towed our fifth wheel over the Bighorns from I-90, then on to Cody and Yellowstone. We took the more scenic U.S. 14/14A route instead of U.S. 16 because we wanted to stop at Bighorn Canyon National Recreation Area. But we have a diesel and an exhaust brake that we used all the way down the 6-mile long, 10% downgrade on 14A. We stayed at the beautiful Sibley Lake Forest Service campground (with 30A electric hookups) on 14.
However, I agree with the others that once you have traveled east to west over the crest of the Bighorns, it is a waste of time to go back down to the east. And on 16, it is no steeper downgrade going west than going back east.
If you do use I-90 through Billings, it is quicker to Yellowstone through Mammoth and the North Entrance than all the way around to West Yellowstone. And, having driven the Beartooth Highway (U.S. 212) from Cooke City to Red Lodge, I advise against taking any large RV from Red Lodge to the Northeast Entrance to the park. The hairpin curves on the switchbacks are VERY tight and the lanes narrow! Guess that's why, like U.S. 14A, U.S. 212 over Beartooth Pass is closed in winter.
"Retirement is the best job I ever had!"
2015 RAM 2500 4x4 crewcab 6.7L CTD; 2016 Rockwood Signature UltraLite 5th wheel