No not really. We have wind on the Earth because the Earth has strong enough gravity to keep gas on its surface (not all gasses though, really lights ones like hydrogen and helium can escape the atmosphere and go out into space). It’s these gasses (nitrogen and oxygen, mainly) that move about the Earth’s surface and make us feel the wind.
The moon is much smaller than the Earth, and has much weaker gravity (1/6th as strong, from the top of my head). That means that it can’t keep most gasses on its surface, which means there’s nothing to make ‘wind’ with.
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