I am writing an essay which involves many concepts supposedly unfamiliar to the reader. It has been suggested to me that the explanations of these terms be in the footnotes as this way they wouldn’t count towards the word limit.
My preferred style is the MLA, which doesn’t seem to have a custom of such. Which style should I be using if I intend to put in extensive explanatory footnotes?
While there are sometimes writing assignments in university courses with some strange rules for computing the word-count, as a general practice, the decision of whether to put information in the body of a paper or its footnotes (or an appendix or elsewhere) should be made on the basis of readability and convenience to the reader. The decision should hinge on what is the best way to present information to the reader (and perhaps also stylistic consistency of particular journals, etc.), not on the basis of some silly idea that words in a particular area don't count against a word-count restriction.
There is nothing inherently wrong with having extensive footnotes in a paper if this is the best way to present information to the reader. Generally this will occur where there are lines of argument or observation that are ancillary to the main thrust of the paper, which would distract from the flow in the body of the paper. Nevertheless, I would counsel strongly against moving material to footnotes merely to try to abuse a set of silly rules relating to word-count. (If this paper is for a university assignment, and your lecturer has imposed a set rules that incentivise this, please feel free to draw their attention to this post to let them know that they are engaging in poor educational practice.)
As to what you might call a writing style that focuses on doing this, I would call it the style of bad writing.
As far as I am aware (but I could be wrong), there is no academic journal or book publisher that does not include footnotes into the total word length. Even if this is an essay, it is highly likely that your teacher also considers footnotes as part of the total word length. I advise you to confirm such details with the person in charge of the course.
There is no fundamental relationship between a citation style (or manual of style) and the length of footnotes. It depends on the topic that is being handled, and the chosen method of research. Longer-than-usual footnotes are more closely associated with certain research fields, especially within the humanities.
The most common use of extensive footnotes can be found in critical editions of pre-modern, medieval and ancient authors. A good example is the critical edition of the Dead Sea Scrolls, and a more recent example would be Sonu Shamdasani's annotated edition of Carl Jung's Black Books.
Related to this, we can find academic journals that allow for extensive footnotes (within reason), depending on the topic: studies of pre-modern legal history, religious texts, archaeological finds, medical treatises, ancient architecture, etc. One journal that tends to allow for large footnotes is Monumenta Serica (example 1) (example 2).
Lengthy footnotes tend to become unavoidable when one is dealing with cultures that are profoundly different from modern ones, or when dealing with artefacts and documents that go back far in time. Other fields such as philosophy can also sometimes have unusually long footnotes. Again, it depends on the topic that is being analyzed.
However, it is important to stress that one should make every possible effort to avoid long footnotes, even when it is allowed. For example, make a list of the topics or concepts that require the longest explanations, and create a section near the introduction that provides a basic, clear and simple explanation of such concepts. Then, when you need to add more nuance or minor details to those explanations, use footnotes. Or try to spread the explanation of those concepts throughout the text, while still using footnotes for small details. At every stage of the process, ask yourself: "Is this explanation really necessary for a reader to understand the key points of my essay?" Train yourself to write clearly and concisely, because that is one of the main reasons why students are asked to write essays.
One last word regarding styles. It has become fairly common to use Chicago (or adapted versions of it) in books with extensive footnotes, not because it encourages such long footnotes, but because it is designed to provide detailed referencing data for finding old documents in historical archives. Chicago is extremely useful when you need to distinguish between different manuscript copies or versions of the same text, which can be spread over different archives around the world.
So far as I know, every style can accomodate footnotes. You don't often see them used extensively, in the way you're asking about, because it makes for tedious reading.
Legal studies articles sometimes include extensive footnotes. For example, Marco Jimenez's article "Finding the Good in Holmes's Bad Man" in Fordham Law Review (Volume 79 Issue 5 Article 9) includes multiple pages that are 75%+ footnotes as well as one page (2075) that is entirely footnote overflow from the previous page! Many of the footnotes are case citations as would be expected, but quite a few include extensive commentary on the case as well that the author didn't feel quite fit in the body of his article.
I own a book, First Peoples in a New World, David Meltzer, that is a popular rendition of the scientific literature of the archaeology of what became the Americas from around 12,000 or so years ago. It is around 20% endnotes. Meltzer is one of the developers of some of the main theories of people from that time up to, say, the neolithic.
However, of you want to read it all, including the scientific notes, it is maddening to read, though very informative.
As a print book, the notes are certainly contributing to the word/page count, of course.
But, other books, those that merge a popular and a theoretical/scientific view into one work, probably satisfy your search for a "writing style". But that is much less likely to be used in an essay or paper.
I was taught that footnotes are bad and disrupt the reading flow. One should probably omit them alltogether, and with some writing discipline this is doable.
Now, speaking of the "oh, and by the way" notices – which you would rather write in a book or maybe a thesis, but not in a research article – I see two ways.
The more conventional one is to create a separate section and put all the trivia there. The other one leans on Knuth and Tufte and is more a presentattion thing: use extensive wide sidenotes, such as those in tufte-latex class. Put the trivia in there, without footnote symbols or anything. In this manner the trivia would not disturb the reading flow, the presentation of actual material.
