Is cow ever the plural of cow?

This may be an issue with instances of cow used as an attributive noun modifying another plural noun, whether a class that takes a regular plural (e.g., animals) or not (e.g., elk):

... a herd of cow elk ...
... a field of cow animals ...

When I did a search for "herd of cow" I turned up exactly that kind of result.

Google's NGram search has many notable problems, of which this is one. See my post on EL&U Meta about NGram searches, the point being that there are many kinds of terms that seem to invalidate statistical support from the Corpus. Personally, I use the tool but am very wary about the results. Unless the search terms can be sufficiently sanitized, I can't draw any conclusions.

English ‘Irregular’ Plurals

The poster writes:

“I noticed that, unlike with sheep or deer, cows is the plural of cow. I started wondering why”

However, this seems to assume that English has some rule for forming plurals of words on the basis of the class of objects described — in this case animals (or even ruminants!), and ignores the facts that the ‘irregular’ plurals of very old words in the English language reflects their individual development from Germanic Old English forms. In most cases such Germanic plurals were replaced, sooner or later, by the plural in ‘s’, the persistence depending to some extent on frequency of usage in the language.

Germanic plurals (which varied with case) were made by different word endings (often e, en or n) or changes in vowel, or both. Examples of words in which these survive include:

ox — oxen
brother — brethren
man — men
mouse — mice

It can be seen that such plurals that survive in English involve a vowel change or a final ‘n’. Other endings have disappeared entirely, leaving singular and plural identical, these not only include ruminants, but fish such as:

fish
trout
cod

So what precursors or regional variants does ‘cows’ have?

The first point to make is cow had a plural with both a vowel change and final ‘n’ — kine —which although now archaic, persisted for a long time before being displaced by the ‘regular’ English plural, ‘cows’. For example The King James Bible refers to:

“Thirty milch camels with their colts, forty kine, and ten bulls, twenty she asses, and ten foals”

(Genesis 32:15)

And the OED (Oxford English Dictionary) contains a reference to Kine-Pox (Cow-Pox) in a book title from 1800. According to the OED, the plural cows “hardly appears before the 17th c”.

But are their other variant plurals, perhaps regional, as the poster asks? I would regard the OED as a better source in this respect than Google books, as it tends to quote such variants, but the only variant plural mentioned is ky or kye in the North of England and Scotland.

So there is no reason to expect a plural ‘cow’ and I do not believe one exists.

Footnote: “A chasing the deer”

The OED lists a variety of examples of Old English plurals: deor, deoran and deore, and in early Middle English (1250 and later) mentions examples of plurals with ‘s’ — deres, dueres. The form without an ending must have been sufficiently entrenched to resist the tide of change.