Helmet when hunting?

[Iron Glove]

If it’s a forest service road you need to have insurance to operate a ATV on. For your insurance to be vaid you need to be wearing a helmut. So yes you could get a ticket for no helmut on a FSR as you would technically not have insurance at the time.

On a spur road or private property you don’t need insurance so you don’t need a helmut.

I don't think that is quite correct.
The only insurance that is mandatory to ride where it is required is Third Party Liability, i.e. if you, as the operator / owner of the ATV injure someone or damage property.
It does not cover an injury to yourself.
I believe your liability insurance would still be liable unless it could be proven that the proximate cause of the injury to others or damage to property was your not wearing a helmet. Even then that might be a tough one for the Insurers to do.
It's kinda like you have to wear your seatbelt while driving your car. If you smack somebody or another vehicle while not having your seatbelt done up it should not invalidate your policy. You can be ticketed of course.
If you insure your ATV and you have accident insurance covering you, then yes, you might not have any coverage for your own injury.