Cold air intake

Agree. By itself you likely won't notice the difference. I would expect less than 10 HP. If you want significant performance gains go to someone like ZZPerformance and see what's available.

The only thing you will notice is the reduction of cash from your wallet. Think about it. The theory is sound (colder, denser air burns better when mixed with fuel) but is the air you will get into the combustion chambers be any cooler than it is now? Unless the air source is altered to find a different air flow pattern or the filtration system provides a less restrictive air path to the intake manifold, you will see no change in useful HP.

Which is exactly what a CAI does, so I’m not sure what you’re point is.

My point is these systems typically don't grab any colder air unless the intake snout is positioned away from the engine. If you do anything with the engine's air supply, find where you can position the intake as far as possible from the engine heat and can flow the greatest air volume into your engine with the least resistance from tubing bends and restrictive filters.