The change in surface coloration that you see on your gate is called a patina. It occurs on metals like copper and its alloys due to exposure to various atmospheric elements. The color of the patina depends not only on the underlying metal/alloy but also on the elements/compounds that caused it. When the patina is green, it's often referred to as verdigris. Brass and bronze, which are copper alloys, can definitely develop verdigris. For example, here are some brass fittings that were exposed to saltwater and air:
And here are some bronze cannon barrels with a nice verdigris:
For something like an exterior gate, wrought bronze would be a more typical material than copper.
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