Unity3D Cameras

I am creating a horse racing game. I have 10 horses per race and fooling around with multiple cameras that can be changed during the race. For instance you can have a camera chasing any of the 10 horses from behind.

The only way I can currently get it to work and it works great is by creating 10 camera objects and in design mode positioning and parenting each camera behind its horse object. Camera1 to Horse1, Camera2 to Horse2, Camera3 to Horse3 and so on. Only 1 camera is active at a time (of course) while the other 9 camera active properties are set to false. I am setting the active properties via script and its working great.

I would love to keep it this way as its working flawlessly because Ive tried to only have one camera and tried to script that camera to parent to either horse during the race but its just never at the right position with whatever code I try to modify.

My question is:
Will having 10 different camera objects even though only 1 is active at a time punish the performance as I continue to develop my game with more assets and scripts?

 

If you camera is disable this wont render anything and have not any perfomance penalty, i have try this with more that 1000 cameras at time.

 

Thank You, PrefabEvolution for the generous and quick response! I'm gonna end up having about 20 cameras and now I'm not worried at all.