The byline to Jacula Prudentum reads "Selected by Mr. George Herbert, Late Orator of the University of Cambridge," and a note attached to an 1881 edition of the collected works of George Herbert says this:
It has been objected that there is no absolute proof that the proverbs [in Jacula Prudentum] were translated by Herbert (see “Notes & Queries,” second series, No. 57, p. 88), but these objections were ably set aside by Mr. Mayor in the same series, p. 30. It appears that Herbert’s works were held in high esteem and kept in MS. At Little Gidding, from whence Dr. John Mapletoft derived his two MS. Collections of proverbs, one of which professed to be a work of Herbert’s. There is, therefore little reason to doubt that he [Herbert] was the translator and editor of them.
As ermanen suggests in a comment above, if the English trail of the proverb ends at Herbert—either as author or translator from another language—it follows that Herbert is the source, in English at least. And indeed there is a related French proverb (discussed below), though it is not at all a literal counterpart of “Milk says to wine, Welcome friend,” but a possible source nonetheless. I haven’t been able to find any source in English that antedates Herbert.
Early attempts to categorize or characterize the saying
William Hazlitt includes the phrase “Milk says to wine, Welcome friend” in his relatively systematic and well-organized English Proverbs and Proverbial Phrases (1869), but in discussing Jacula Prudentum, Hazlitt is not especially charitable:
The volume of Outlandish Proverbs ascribed to George Herbert, whose authorship, I respectfully submit to be rather questionable, and printed in 1640, 8vo. is a meager and insipid business enough, and the pious compiler, if it be his, seems to have omitted purposely (which was so far natural and proper) all the gross sayings, however characteristic, which were current in or before his time, and even to have softened down such as were exceptionable in his eyes, and he did not resolve to exclude. The latter was scarcely a judicious compromise.
The Outlandish Proverbs exhibit one weakness which I have found to be common to all the collections : the confusion of proverbs with mere precepts or maxims destitute of proverbial significance and character.
W. Anderson O’Conor, “On Proverbs,” read on November 17, 1879, and included in Papers of the Manchester Literary Club (1880), sees this proverb and others in Herbert’s collection as representing a stage in the historical development of the proverb:
The passage from sayings of general application to those of a distinctly metaphorical character was natural. One or two examples taken from George Herbert’s Jacula Prudentum will illustrate them. “He stands no securely that never slips.” “The chicken is the country’s but the city eats it.” “After the house is finished leave it.” “Milk says to wine, Welcome friend.” “Diseases of the eye are best cured by the elbow.” “They that hold the greatest farms pay the least rent.” “Old camels carry young camels’ skins to the market.” The proverbial expression has grown here into a parable or dark saying, which is intended for solution rather than guidance, and which affords an exercise for ingenuity rather than an instruction to be practiced. Commonplace observations of life are knotted into enigmas, and wisdom is made to consist in a dexterous untying of them.
Though treating certain proverbs from Herbert’s collection as riddles may be defensible, doing so understates the extent to which they remain statements of folk wisdom. But what is the folk wisdom in “Milk says to wine, Welcome friend”?
Meaning of the proverb
My first thought was that milk was welcoming wine as a friend because both were agents of health in a human diet—rather as if one doctor were greeting a respected colleague. But that idea runs into some problems elsewhere in the land of proverbs.
The “milk says to wine” proverb also appears in [Robert] Southey’s Common Place Book, third series (1850). However, Southey also cites another saying from Herbert’s collection:
A morning sun, and a wine-bred child, and a Latin-bred woman seldom end well.
This saying is no less opaque than the “milk says to wine” proverb, especially with regard to the idea that a morning sun seldom ends well, unless it be that sunset inevitably comes to even the brightest morning (which hardly discredit the bright morning, in my opinion). The troubled future predicted for a "wine-bred child" at the very least suggests that the author of this proverb doesn’t consider milk and wine to be interchangeable in a child’s diet. The "Latin-bred woman," meanwhile, seems to refer to a woman who has received a sound and scholarly education—a potential source of friction in a society that prefers women to be intellectually submissive and unambitious. There is certainly no hint in the "wine-bred child" adage of a happy friendship between milk and wine.
Another perspective on the question arises in William Benham, Cassell’s Book of Quotations, Proverbs and Household Words, revised edition (1914), which repeats the “milk says to wine” proverb and then adds a cross reference to the following saying from John Ray, Compleat Collection of English Proverbs:
If you would live for ever/You must wash milk from your liver.
Vin sur lait, c’est souhai;/Lait sur vin, c’est venin.
—Wine on milk is desirable; milk on wine is poison.—(Fr.)
Wein auf Bier rath ich dir, Bier auf Wein das lass acin.
—Wine upon beer I counsel thee; beer upon wine, let that be.—(Germ.)
And Godfrey Baseley, A Country Compendium [combined snippets] repeats the French saying about wine and milk and then follows it with a new and very brief saying about the two:
Wine on milk is desirable, milk on wine, poison.
Milk welcomes wine.
The Benham and Baseley sayings suggest that the crux of the “milk says to wine” proverb may be that if you drink first milk and then wine, your stomach will accept the newcomer calmly; but if you reverse the order, your stomach will rebel.
Ray’s “wash milk from your liver” proverb—though it may just be a very loose translation of the same French proverb that yields the “milk on wine, poison” adage, seems to go a step further and suggest that something—whether wine or water or some other fluid—is necessary to wash milk from your liver, to avoid bad results from the milk. Ray himself, however, seems to have viewed the “wash milk from your liver” saying with considerable skepticism. In his comment beneath that proverb (which he identifies as “Gallic) from the 1678 edition of his book, he remarks:
This is an idle old saw, for which I can see no reason but rather for the contrary.