COWS is an annoying mnemonic, since you have to understand a whole lot just to use it.
What you are testing is cranial nerve 8. In some one who is awake, you test this by having them look at the ceiling at a fix point while you rotate their head. If their eyes stay fixed, they have intact cranial nerve 8. If their eyes move with your movements of their head ("Dolls Eyes") their cranial nerve 8 is broken.
COWS is used to assess some one who is unresponsive. It tells us two things. First, it tells us if the cranial nerve is intact. If there is a slow component towards the lesion then the cranial nerve is intact. Secondly, it tells us if the cortex is intact. If there is a fast component away from lesion then the cortex is intact. If there is no movement at all, then the cranial nerve itself is lesioned.
Lets handle the CO of cows. You inject cold water into an ear. You inject cold water onto a cranial nerve. Now, cold water makes things cold. Cold water makes things not work. So, with cold water, you induce a cranial nerve 8 lesion. That means, if the cranial nerve is intact, there is a slow movement towards the side you squirted water in. If the cortex is intact, there will be a fast movement away (following the slow towards) from the side you injected the water in. If the cortex is not intact, but the cranial nerve is, there is only a slow towards, and no away. If there is cortex, but no cranial nerve, then nothing happens.
Lets handle the WS of cows. This is harder to understand. Lets say that you have two normally functioning cranial nerve 8. By adding warm water you increase the activity of the side you squirted the water into. Warm water makes things work better. This means, relative to the side you stimulated, the opposite side represents the induced "lesion." If you followed the CO example well, you know exactly what happens. There is a slow component towards the lesion (which means away from the warm water injection) then a rapid component away from the lesion (which means towards the warm water injection).
So "COWS" actually referrs to the direction of eye movement during the fast away-from-the-lesion component following the slolw-towards-the-lesion component in someone who has an intact cranial nerve 8 and intact cortex. See why that is a confusing (and somewhat useless) mnemonic?
If you really want to take something away from COWS, and dont care to reread (or understand) my response, take this. COWS represents the direction of the rapid eye movement relative to the injected water; a cold water injection has a fast component opposite the injection while a warm water injection has a fast component that is to the same side as the injection