To move your horse from one area into another first visit your horses profile.
Scroll down the page until you see the side panel titled "Stabling".
This panel is a summary of the area the horse is currently living in, and what farm that area is located at. You can also see how many horses are living in this area, and what the grass quality is.
At the bottom of this panel is a dropdown list of all the areas on your farm where you can move your horse into. If an area is full you won't be able to choose to move your horse into that area.
Its important to remember that a pregnant mare uses 2 spaces in an area, one for her and one for her foal.
