Is an object acted on by either horizontal or vertical forces?
An object can be acted upon by either horizontal or vertical forces or both forces at the same time. Even at a state of rest, any object on planet earth feels a downward force. This vertically downwards force is due to the gravitational pull of the Earth on the object. And this is the very reason why everything falls downwards (when no other force is acting on it; conversely we will need another force to prevent objects from falling down).
Horizontal force can be applied by someone or something on an object, be it wind gust or machine push (or pull). If one is pushing a book along a table, horizontal force is being exerted on the book. One can throw a ball at some angle and the ball will feel both a horizontal component of the force as well as a vertical component of the force at the same time.
Hope this helps.