You can access the Beauty Salon by tapping on the color icon at the bottom of the screen and then the button with a hoof and a bow.
Tapping on different bows in the Beauty Salon will allow you to see what the bow will look like on your horse.
You can have your horse wear the bow right away, but otherwise, all of your bows will be stowed in the Inventory.
If you want to change your bows, select the horse you want to dress up or whose bows you want to change and return to the Beauty Salon, where you will see the bows you can get and the ones you already own.