In order to run Horizons on your steam version of elite dangerous you'll need to navigate to the folder where Elite Dangerous is installed.
In your library right click on Elite Dangerous and click properties.
Click Local Files Tab.
Click Browse local files
Double click EDLaunch.exe
The ED launcher should open but instead of orange and black the color scheme will be blue and black. IF you have horizons on your account it should pop up in the list of elite dangerous titles. You shouldn't have to download anything just select Elite Dangerous 64-bit horizons and click play.