Sure, maybe this movie would be best described as a Drama - and it is a Drama - but I also feel it could be described as a horror movie. My reasoning is based on what the characters experience (which in turn you experience): horror of loss, horror of memory, horror of the reality.
The Brown Bunny is slow by most movie standards - but this slowness is necessary to tell the tale appropriately. Let me share with you what the movie cover has to say:
"Adults Only: Raw, Tender, Brutal. The Brown Bunny is both a love story and a haunting portrait of a lost soul unable to forget his past.
After finishing a motorcycle race in New Hampshire, Bud Clay (Vincent Gallo) loads his racing bike into the back of his van and begins a cross-country odyssey to Los Angeles, where he is to compete in another race. During his trip, he meets three very different women: Violet, a wholesome all-American gas station attendant; Lilly (Cheryl Tiegs), a fellow lost soul he connects with at a highway rest stop; and Rose, a Las Vegas prostitute.
Throughout his journey, Bud can never escape his intense feelings for the love of his life, Daisy (Chloe Sevigny), so he plans to reconcile with her when he reaches Los Angeles.
Arriving in Los Angeles, Bud checks into a motel before visiting the abandoned home he once shared with Daisy. He leaves a note, hoping she will turn up at his motel room...
Building to a notorious climax, the film presents one of the frankest portrayals of male sexuality ever seen in American cinema."
No you go watch it.