After reading the whole of Margaret Bertha Wright's article, I can confidently say that all the (now deleted) speculation here pertaining either to 'mad cow disease' (bovine spongiform encephalopathy / BSE), or to the dining facilities aboard Victorian-era English trains and what victuals might be served there, is misplaced.
Margaret Wright's article makes great play of the social embarrassment of the British artists inhabiting the Cookham Dean artists' colony at actually either being impoverished, or fearing that they might be perceived to be so.
Wright contrasts their attitude with the less wealth- and status-conscious visiting Continental artists who are also staying there, and some of whom regularly have to pawn their valuables to make ends meet. To begin with, says Wright, the Continentals feel no inhibition about confessing to this practice. But soon the English mentality of being ashamed of one's poverty starts to infect them too:
It may be observed, however, that here, as everywhere else in this right little tight little isle, where habit is the very antithesis of the airy license of "Abroad," it is not, as it is in the artistic haunts of the Continent, en règle [socially acceptable] to vaunt one's self on the paucity of one's shekels or to acknowledge acquaintance with the Medici's pills in their modern form of the Three Golden Balls. [the traditional emblem of the pawnbroker's shop.]
Once upon a time, in a Barbizon auberge, a certain famous artist and incorrigible Bohemian brought down the table by describing an incident of his releasing a friend's valuables from durance. [captivity in a pawnbroker's establishment.]
"The moment I turned in at the Mont de Piété," he said, "my watch took fright, and stopped ticking on the spot."
That same Bohemian, after years of the Latin Quarter and Mont de Piété, found himself one summer on the Dean. One evening at the porch of Ye Hutte [a large shared artists studio] he met a lively group of painters and paintresses, just returned from corn-field and meadow.
During the short halt the Bohemian's watch was so largely and frequently en évidence as to attract attention.
"Yes," he said, with colossal, adamantine impudence, "I've just got it back from a two-years' visit to 'my uncle'." [the pawnbroker.]
Only a few evenings later the same party met again in the same spot.
"What time is it, Mr. S——?" asked Sophia Primrose, amiably disposed to resuscitate a forlorn joke.
A mammoth blush submerged the luckless Bohemian. For Dean propriety was already becoming engrafted upon Continental habit, and he crimsoned at having to confess what once he would have proclaimed upon the house-top,—that his watch was again with his "uncle."
Probably nine-tenths of the Continental artists who are not entirely beyond the dread of yet eating "mad cow" travel third-class. But Dean artists, however they may travel when out of England, generally slip quietly away from the sight of their acquaintances when their tickets are other than at least second. Our Bohemian was once presented with a second-class ticket to London. As he scrambled in upon the unwonted luxury of cushioned seats, he saw familiar faces blushing furiously.
"The first time we ever travelled second-class in our lives," murmured Materfamilias. [Presumably from embarrassment at finding herself seated alongside someone that she regarded as her social inferior.]
"I too," responded the cheeky Bohemian.
I found another reference to 'eating mad cow' in a French novel titled The Conscript, written by Emile Erckmann and Alexandre Chatrian in the 1860s and published in an English-language translation in 1908:
Then the old soldier said to me—
"You are going to rejoin?"
"Yes, the 6th, at Torgau."
"And where do you come from?"
"From Leipsic, out of hospital."
"Yes. one can see that," said he; "you're as fat as a dean. You've been fed on legs of fowl down yonder while we've been eating mad cow."
I looked at my sleeping neighbors, and I saw that he was right. These poor conscripts were reduced to skin and bone; they were yellow, and lined and furrowed like veterans; one would have thought that they could never hold out longer.
Evidently, the expression 'eating mad cow' probably had more to do with living in a state of poverty in a general sense than with the actual nature or composition of one's diet. Hence 'to eat mad cow' in the context of these texts simply means 'to be on one's uppers', 'to live like a pauper'.
So the author's observation that Probably nine-tenths of the Continental artists who are not entirely beyond the dread of yet eating "mad cow" travel third-class is a reference to the fact that 90% of those Continental artists who fear being reduced to poverty decide to travel by the cheapest possible means, i.e. in a third-class railway carriage.