There isn't a magazine size restriction for hunting big game. The restrictions we do have are listed below:
IDAHO WEAPON RESTRICTIONS
Rifle and Shotgun
In any hunt, including any-weapon seasons, it is unlawful to pursue or kill big game animals:
• By any means other than approved firearms, muzzleloaders and archery methods.
• With any electronic device attached to, or incorporated on, the firearm or scope; Except scopes containing battery powered or tritium lighted reticles are allowed.
• With any firearm that, in combination with a scope, sling and/or any attachments, weighs more than 16 pounds.
• With any fully automatic firearm.
• With any shotgun using shot smaller than #00 buck.
• With any rimfire rifle, rimfire handgun, or muzzleloading handgun, except for mountain lion.
In big game seasons restricted to short-range weapons, it is unlawful for hunters to use any weapon other than a muzzleloader, archery equipment, crossbow, a shotgun using slugs or shot of size #00 buck or larger, or a pistol using straight-walled cartridges not originally developed for rifles.
Muzzleloader Caliber Requirements
In any hunt, including general any-weapon seasons and short-range hunts, it is unlawful to pursue or kill big game animals:
• With any muzzleloading rifle or musket that is less than .45 caliber for deer, pronghorn, or mountain lion; or is less than .50 caliber for elk, moose, bighorn sheep, mountain goat or black bear.
Any person hunting in a muzzleloader-only season, including controlled hunts must have in their possession a license with a muzzleloader permit validation. During a muzzleloader only season, it is illegal to pursue or kill a big game animal with any firearm, muzzleloading pistol, or weapon other
than a muzzleloading rifle or musket. In addition, the muzzleloading rifle or musket must be:
• Capable of being loaded only from the muzzle.
• Equipped with only open or peep sights. Scopes and any electronics are prohibited. Except hunters with a visual disability may apply for a permit to use nonmagnifying scopes. (Applications are available at Fish and Game offices).
• Loaded only with loose black powder, loose Pyrodex, or other loose synthetic black powder. Pelletized powders are prohibited.
• Equipped with a single or double-barrel.
• Loaded with a projectile that is within .010 inch of the bore diameter. Sabots are prohibited.
• Loaded with a patched round ball or conical non-jacketed projectile comprised wholly of lead or lead alloy.
• Equipped only with a flint, percussion cap or musket cap. 209 primers are prohibited.
• Equipped with an ignition system in which any portion of the cap is exposed or visible when the weapon is cocked and ready to fire.