There is also a biological response that happens when a person's mouth and nose are covered in water, since being covered in water generally means not being able to breathe.

Said response isn't in fish.

An ice cube down your shorts will wake you up, but that's not something a fish would have a natural reaction to. Temperature seems the more plausible explanation.

Also, cold water specifically wouldn't mean much to an aquatic animal that lives in that water. It's basically the same as its body temperature, so the human equivalent would be washing your face with 37C water.