No, it is not possible to get a moon tan or moon burn. Moonlight is simply reflected sunlight, and its intensity is significantly lower than direct sunlight. The moon's surface reflects only a small fraction of the sunlight it receives, making it much dimmer than sunlight on Earth.
Sunburns or tans occur due to the ultraviolet (UV) radiation present in sunlight. However, the moon does not emit UV radiation, nor does it reflect enough UV radiation from the Sun to cause any significant effects on human skin.
It's important to note that even though moonlight is relatively dim, prolonged exposure to the Sun's direct rays, even during moonlit nights, can still result in sunburn or tanning. Therefore, it is advisable to take appropriate sun protection measures when spending time outdoors, regardless of whether it is during the day or under moonlight.