I guess it might technically work, though it certainly doesn't sound as natural.
Would "wohin" versus "wo" make a difference in the meaning here? I read two possible meanings, corresponding to (1) the location of the moon in the sky and (2) your location on earth when you see the moon.
Wohin basically means "to where" (like "woher" means "from where"). As christian said, it's "wo" in both cases, because it refers to a fixed place, not motion/traveling.
It's "wo" in both cases. "Wohin siehst du den Mond" doesn't make any sense.