Musically, "Cinnamon Girl" seems to showcase both of Neil Young's most famous modes: dirty, driving, grungy rock, and a romantic, almost ethereal, melody. Since I don't understand much technical musical theory, I don't really have a theory on how Neil Young pulled that off.
The lyrics of the song follow the same dichotomy. The song in most ways seems to be a pretty straightforward love song about Neil Young's wish to find happiness with "the cinnamon girl". However, the song's imagery and emotional tone are somewhat elusive, and if a listener wishes to, they could find something almost sinister there. It occurred to me, as a teenager, that this song might have been a drug song, and apparently, I am not alone in speculating about this.
This speculation seems to be based around the title of the song and several lyrics. "Cinnamon" could refer to the color of hashish or black tar heroin. The song speaks about "chasing the moonlight", which sounds similar to "chasing the dragon", "the drummer relaxes, and waits between shows for his cinnamon girl", which sounds like a musician getting high between shows, and "pa send me money fast", which sounds like someone pleading for money to get high. But while these words by themselves might sound suggestive, putting them together involves a lot of invention. What exactly, are the "ten silver saxes and a bass with a bow"? syringes? pipes? spoons?. If the drummer is waiting for heroin, why is he relaxing? That is the opposite of how people act when anticipating heroin. And when have either hashish or opiates lent themselves to late night jogging? Although the song's lyrics are certainly open to interpretation, trying to guess at it being a "coded message" seems to involve having to shoehorn a lot of things into place.
Poking around online, I found a lot of rumors and speculations about what this song is about. This is especially so because Neil Young's creative process is opaque, even to him. One report says this song was written in a fever dream, which is especially interesting because fevers can trigger seizures, and Neil Young is epileptic. To me, it is almost like this song is about, and created by, the creative process itself, as the artist tries to chase creativity, illuminated only by the moonlight, but that is just speculation. Unless Neil Young himself wants to come out and give us a definitive cliff's note explanation of the song (and if he, himself, can even remember after 50 years), it seems the easiest explanation is that this is just a romantic song with a dash of psychedelia thrown in.