I've found one big horn in NA and that was after working on challenges and very few of the story missions since Tuesday afternoon. I'n guessing it was just a fluke and they're in West Elizabeth.
I Haven't unlocked West Elizabeth yet, and i know for certain I've encountered a big horn.. I'm pretty sure it was in northern Mexico.
If you look at your map (the paper one) you'll see that there's a bighorn symbol hidden behind the Rathskellar Fort symbol. You may find some there. As for Elk, I never saw any in New Austin, and despite searching for days where they're marked on the map, I never came across one in Mexico, either. They seem to be pretty exclusive to the Tall Trees area (and once there, you can miss them. They're everywhere... Along with the bears.) You might find them in other areas of West Elizabeth, but why bother when you almost trip over them in Tall Trees and Nekoti Rock?