You will need to purchase feed at the market and then return to your horse's page to change the feed.
Getting the feed: Click on the market icon. On the Buy section click on the Feed button.
Select the feed and type (or use the plus sign) to set the quantity you would like to purchase and then click the Buy button. Changing the feed: You must go to your stable (by clicking on the icon) and select the horse you wish to feed.
Then just click the Feed horse button and select the type of feed you have from the list.