Depending on what part of the Mojave you were in, there can be more older stuff than younger stuff. (There were a lot of Pleistocene lakes back in paleo times.)
Not sure about the horn, but they usually don't last long when exposed to the elements. I'd guess it's from within the last 20 years. You should be careful with the sheep horn. In some places is was a huge no-no to pick up the skulls or horns, other places you could but you needed to take them to the Fish & Wildlife office within so many days to have them document it, in some places you could take it if it was detached from the skull like yours is. Not sure about your area. (A google search should produce lots of results for you.)