When you approach the horse, it may become visibly active and show changes in its posture. Its ears will likely be pricked and forward, its neck arched, and its tail may be lifted. Additionally, the horse may start to nicker and move its head around in anticipation.
It may start to paws its front or hind legs, or even move backwards or create other movements. Another clue is if the horse starts licking its lips or blowing through its nostrils in an exaggerated manner.
All of these behaviors span across species and indicate that the horse is feeling excited to see you.