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Possession No state permit is required to possess a rifle, shotgun, or handgun. It is unlawful for a minor (a person under 18) to go armed with a handgun or for any person to sell, lend, or give a handgun to a minor. This does not apply to target shooting when the minor is under the supervision...

The marines test ammo at all different extremes in temp to ensure consistant accuracy, so I don't believe the cold would be a major factor. My concern would be keeping the powder dry. You would almost have to engineer a refridgerated weapon to maintain the subfreezing temps required.