Profit: None; doesn't make any produce.
Care: Be sure to talk to your horse and talk to it every day (or as much as you can). You don't need to worry about feeding it, though. Once it matures, you can buy a saddle bag for your horse and have the option of riding it around. The saddle bag is very useful to have because you can put crops/items in it and those things will be automatically shipped. It serves as a mobile shipping bin.