ClickDetector is not a valid member of ClickDetector?

Every script is given a variable to represent itself as an object in the hierarchy, called script. The parent of the script, script.Parent, is the object which script is a direct child of. In other words, it tells you what the script is in, such as a ClickDetector. script.Parent == the ClickDetector that the script is in. So, if you say script.Parent.ClickDetector, you're trying to access a ClickDetector within that ClickDetector, which isn't there.

On the last line, replace script.Parent.ClickDetector with script.Parent.

Now your script does not error, but your shower won't turn off. Let's see why.

Sprinkle = workspace.Shower.Shower.ParticleEmitter1
local cold = false

function onClicked()
    if not cold then
        cold = true --But it never becomes false if it's true!
    end


        if cold == true then
            Sprinkle.Enabled = true
        print("On")
        end


        if cold == false then --The following code will never happen!
        Sprinkle.Enabled = false
        print("Off")
    end
    end


script.Parent.MouseClick:connect(onClicked)

Since cold never goes back to false, we can't shut the sprinkler off. Let's fix that.

Sprinkle = workspace.Shower.Shower.ParticleEmitter1
local cold = false

function onClicked()
    cold = not cold --This is a trick to toggle a boolean's state between true and false.

	if cold == true then
		Sprinkle.Enabled = true
        print("On")
	elseif cold == false then
		Sprinkle.Enabled = false
        print("Off")
	end
end


script.Parent.ClickDetector.MouseClick:connect(onClicked)