The moon is often overexposed in night scenes because its brightness is dramatically higher than the surrounding landscape. A moon exposure can leave everything else nearly black, while exposing for the scene turns the moon into a bright, bleeding highlight.

HDR can be used, but it’s often not the best tool here. At night, long exposures make blending difficult because the moon moves, trees or branches may move, and the bright moon can spill into nearby pixels. That can make HDR alignment and blending look messy.

A more common solution is a double exposure or composite: one exposure for the moon, another for the landscape. If the moon doesn’t overlap important scene details, this is simpler and cleaner than HDR. Many published “moon in landscape” images use this approach, even if they don’t say so.

So the short answer is: people do solve this problem, but usually with compositing rather than traditional HDR. Whether that looks unnatural depends on how honestly and carefully it’s done; it’s generally fine for artistic images, but not appropriate for documentary or journalistic work.