This biography of Einstein (exact page) asserts that, and narrates the dream in astonishing detail. The only chance of it being true is a direct testimony of Einstein himself, but I haven't found it.

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    The claim of the supposed dream is repeated "all over the internet." There is also the 1992 novel Einstein's Dreams by Alan Lightman, but it is still subject to copyright and as I don't have access to the full text cannot verify whether this is the true source. – Weather Vane Nov 23 '20 at 17:40
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    That book ("E = Einstein" (2006)) is not a biography but a collection of essays by different authors. The one containing this story is "Einstein's Bovine Dreams" by João Magueijo. It also appeared in his book "Faster Than the Speed of Light" (2003). I'm almost sure that Magueijo simply made it up, and you'll find no references to it earlier than 2003. I checked a few Internet references and those that cited a source all cited E=Einstein. – benrg Nov 23 '20 at 20:37
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    @Fizz From the blurb: I looked for you. "Einstein's Dreams is a fictional collage of stories dreamed by Albert Einstein in 1905, when he worked in a patent office in Switzerland. As the defiant but sensitive young genius is creating his theory of relativity, a new conception of time, he imagines many possible worlds." A quick search doesn't mention cows or electroshocks. The text doesn't seem bad, I might read it. (Hey, does anyone strike it as odd that an teenage Einstein would dream about electrified fences, in 1895 or so? No?) – David Tonhofer Nov 25 '20 at 9:00
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    @DavidTonhofer the "teenage Einstein" of whom you speak so flippantly was working in a patent office because he was waiting for his doctorate to be formally confirmed. – Mark Morgan Lloyd Nov 25 '20 at 22:13
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    @MarkMorganLloyd No. He started at the patent office in 1902, at age 23. But the point is, who delivers electrified fences in 1900? Siemens & Halske-Schuckert? – David Tonhofer Nov 25 '20 at 22:38

According to an article in Nature reviewing Magueijo's earlier book, the story is fictional:

Faster Than the Speed of Light is a lively book that captures the excitement and frustrations of doing real-world science. Magueijo relates interestingly how his VSL proposal might possibly be a way out of some major puzzles facing cosmology, which he explains well. There are irritating passages, however, where he makes extended use of a metaphor involving farmers and cows in explaining relativity theory. Magueijo states that this is based on a dream that Einstein had as a boy — a fictional invention that displays such a cavalier attitude to historical truth as to call into question his other historical claims (and for the record, it was Richard Tolman, not Yakov Zeldovich, who first investigated the thermodynamics of bouncing universes).

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    It's very interesting how misunderstanding sources of information can lead to misconceptions of reality. – RockPaperLz- Mask it or Casket Nov 26 '20 at 0:08
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    @RockPaperLz-MaskitorCasket: I don't think it's that interesting; it's just another drop in the ocean of fake news on the internet... – user21820 Nov 27 '20 at 10:44

No cows but might be the source.

Einstein: An Intimate Study of a Great Man
Biography by Dimitri Marianoff (Einstein' son-in-law), Palma Wayne

"-How is it, Albert, that you arrived at your theory?
-In vision, "he answered."
He said that one night he had gone to bad with a discouragement of such black depths that no argument would pierce it. "When one's thought falls into despair, nothing serves him any longer, not his hours of work, not his past success-nothing. All reassurance is gone. It is finished, I told myself, it is useless. There are no results. I must give up. Then this happened. With infinite precision the universe, with its underlying unity of size, structure, distance, time, space, slowly fell piece by piece, like a monolithic picture puzzle, into place in Albert Einstein's mind. Suddenly clear, like a giant die that made an indelible impress, a huge map of the universe outlined itself in one clarified vision. And that is when peace came, and that is when conviction came, and with these things came an almighty calm that nothing could ever shake again, not while Albert Einstein lives...""

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