The round in line with the barrel is in firing position, regardless of whether it can actually be fired.
However, the prohibition on carrying a loaded gun--without a permit to carry--(as contained in 76-10-505) applies to carrying on "public streets". While that may well be extended to include many public areas, I should think that applying it to remote hunting areas is going to be tough.
There may be hunting regulations that apply to what guns can be carried while engaged in a hunt. Having a permit to carry excuses you from such limits and you can legally carry a self-defense gun, pursuant to your permit, even if it would otherwise be illegal on contrary to DWR regulations to carry it while hunting. For example, carrying a gun on a bow hunt. Without a permit, you or your son is fully subject to any DWR regulations about carrying guns on the hunt.
I am not a lawyer, this is not legal advice, etc.