Many listeners have mistaken this song to be about a drug trip. One of the founding members and writers of the band America Dewey Bunnell claims the inspiration is a real desert near the US Army base his father was stationed at
The song is about a trip though the unforgiving landscape but finding comfort in it. The “horse” represents a means of entering a place of tranquility as represented by the desert
As for why the horse had no name and why it went free after nine days, Bunnell doesn’t have any answers for that.