I came across an interesting reference by a figure dating from either the second or first century BCE, Demetrius, who some have attributed as the Demitrius under whom Cicero studied. He is famous for being familiar with Aristotle's work "Rhetoric" and references it throughout his own writing, "On Style" (Περι Ερμηνειας).
In a fascinating section of this work Demitrius gives instructions on the proper style of letters and correspondence. He describes what he believes is the correct manner of writing correspondence; " A letter’s aim is to express friendship briefly, and set out a simple subject in simple terms" (231).
"(223) We will next discuss the style for letters, since that too should be plain. Artemon, the editor of Aristotle’s "Letters", says that a letter should be written in the same manner as a dialogue; the letter, he says, is like one of the two sides to a dialogue.
(224) There is perhaps some truth in what he says, but not the whole truth. The letter should be a little more formal than the dialogue, since the latter imitates improvised conversation, while the former is written and sent as a kind of gift."
"(227) Like the dialogue, the letter should be strong in characterisation. Everyone writes a letter in the virtual image of his own soul. In every other form of speech it is possible to see the writer’s character, but in none so clearly as in the letter.
(228) The length of a letter, no less than its range of style, should be restricted. Those that are too long, not to mention too inflated in style, are not in any true sense letters at all but treatises with the heading, “Dear Sir.” This is true of many of Plato’s letters, and that one of Thucydides."
"(231) If anyone should write in a letter about problems of logic or natural philosophy, he may indeed write, but he does not write a letter. A letter’s aim is to express friendship briefly, and set out a simple subject in simple terms.
(232) It has its own beauty, but only in expressions of warm friendship and the inclusion of numerous proverbs. This should be its only permitted philosophy, permitted since the proverb is ordinary, popular wisdom. But the man who utters sententious maxims and exhortations seems to be no longer chatting in a letter but preaching from the pulpit."
It is interesting how many of the New Testament epistles and not a few of the Apostolic Fathers's letters fall into these descriptions. For example, Romans and Hebrews in the New Testament, and 1st Clement and the Epistle of Barnabas can very much be described in the words of Demetrius as "not in any true sense letters at all but treatises with the heading, “Dear Sir.” (228). His reference to a letter including expressions of friendship and "the inclusion of numerous proverbs" broadly encompasses some of the more informal pastoral epistles, or the letters of John.
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Aristotle, Longinus, Demetrius, Poetics. Longinus: On the Sublime. Demetrius: On Style (Translated by Stephen Halliwell, W. Hamilton Fyfe, Doreen C. Innes, W. Rhys Roberts. Revised by Donald A. Russell. Loeb Classical Library 199. Cambridge, MA: Harvard University Press, 1995), 477-483
