We went last year and the Lamar Valley road was closed so we couldn't get out the N/E entrance. I've been over Beartooth pass a couple of times. That is the best most scenic drive to get into or out of Yellowstone. It was a bummer to be blocked away from the big bison herds in the Lamar.
As to firearms I've never been told anything negative about the rifle I carry in plain view on top of our gear and duffel bags. Never can tell when you might drive up on some idiot being mauled by a bear. When we spent the night in Silvergate MT. right outside the N/E gate we were warned that there was a grizzly pillaging ice chests in the back of trucks at night.
