Yes, but one of the elements of the crime is that you are engaged in hunting. Read the title of the offense. If you are not engaged in hunting, you are not violating this section.
That's not accurate at all. The title of the offense is not the law, and it does not supply any element of the offense. The title is made by the Revisor of Statutes, not the Legislature. The elements are in the body of the statute.
If you break that statute into three parts, it's easier to understand. Section 60-6,342 makes it unlawful to:
(1) shoot, take, hunt, or kill or attempt to shoot, take, hunt, or kill any wild animal or bird from or with a snowmobile; or
(2) carry or possess any shotgun or rimfire rifle while operating or riding on a snowmobile; or
(3) carry or possess ANY firearm, bow and arrow, or other projectile device on a snowmobile UNLESS such bow and arrow or projectile device is enclosed in a car carrying case or such firearm is unloaded and enclosed in a carrying case.
All three of those things are criminalized by the statute, and the 2nd and 3rd have nothing to do with hunting. The only lawful way to have a firearm on a snowmobile is to have it unloaded and enclosed in a carrying case. It doesn't make any difference whether you are hunting or not.
The conservation officer you talked to might not ticket someone for the offense, but it's definitely possible if he wanted to. Don't expect any other law enforcement officer to read that statute the same as the CO. If you are carrying a concealed handgun on a snowmobile, you are breaking the law, period.