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Cartridges are all basically the same. You have the casing, a primer, gunpowder and the bullet. They just come in many different shapes and sizes, so I doubt any one cartridge would differ from another by any noticeable margin (igniting the gunpowder and the bullet leaving the barrel) just due to weather or temperature.
But then there’s of course the matter of how different rounds perform on impact when the target is wearing a winter jacket and so on.