I thinks nowadays it's mostly because we get involved with them from a young age...in movies for example they stand for elegance, wealth but also power. Fans of medieval ages or fantasy have a special love for them and also the people who just love spending time outsode but don't like to be alone (but also don't want to be around people 24/7)
Also for western riding the typical western romance kind of comes in my mind speaking of the draws ^^
Their willingness and loyalty maybe? It’s amazing that horses let us put on saddles and bridles and ride them!! I think it depends on the person and the horse, everyone’s different.