Why? It's a mental state causes by hormones, as a result of (usually external) stimuli, influencing your perception, decision making, etc.
I literally can't think of how "horny" is any less of a valid emotion than "depressed", "stressed", "interested", "fearful", "angry",...
Depressed, and interested are also not emotions. Depressed is a vague term that can refer to a lot of different states. While a diagnosis of depression can be a useful label, a patient describing themselves saying "I'm depressed today" doesn't help them or their therapist, because it can mean so many different things. "Interested" is a thought, not an emotion, and that's the important distinction here. "Stressed" could be an emotion, but it could also be a thought, and is likely both, so it's important to make the distinction.
A lot of people with mental health disorders have a difficult time differentiating between thoughts and emotions. ("Angry" is an emotion, "I want to punch someone" is a thought. We have much greater control over our thoughts than we do our emotions.) When I was in my first psychiatric hospital (Menninger, one of the top in the nation) they had us focus on what they considered the five core emotions: Joy, Sadness, Anger, Fear, and Guilt. Since then I've learned that there's disagreement on what the core emotions are, how many there are, and what to label them, but there seems to be pretty strong consensus that differentiating between thoughts and emotions is important.
Hunger, thirst, pain, heat, cold, and other sensations are also not emotions, even though they're frequently connected to emotions.
Horny often has emotions associated with it, but as a whole it's a combination of thoughts and physical sensations that may or may not be associated with emotions.