[Bruce R.]

That air horn directs cooler air from in front of the radiator to the filter box.....

Without the horn you will suck warmer air from the engine bay. There is a slight reduction in overall efficiency if you run higher intake air temps. Why take the loss?
Replace the intake horn, and when you install it, be sure that the barbs on the horn engage the lip on the intake air duct, or it will keep falling apart. Liquid soap helps with that.

 

[Bruce R.]

As I mentioned, you will lose some efficiency, how much is an open question.....

If there is any way that you can fit the intake to get outside air that is the best thing to do. You will also slightly increase the airflow through the radiator if the intake hole is plugged.
Probably no big deal at all unless you try to get the absolute most out of the engine.