Would it be safe to say that the dog duty and cow duty ascetics were the Indian versions of the Cynics?
There are differences between the two cases.
In Greek philosophy, Diogenes the cynic (or the dog) is described as “Socrates gone mad”, hence in MN57, Punna who behaved like a cow was not described as a naked ascetic, Seniya. In the case of Diogenes, this nakedness is manifested through masturbating in the market place, and his reply typical of cynics: ‘If only it were so easy to soothe hunger by rubbing an empty belly’.
According to the Buddha, both are destined to the company of animals of their choice, or to hell. The above differences though manifested in the way they took refuge: Punna took refuge as a lay follower, and Seniya took refuge as a monastic pending a probation. This seems to be inline with the temperament of each.
The cynics were focussed on this life, whereas the dog-duty ascetic was apparently fully concerned with the next :
“he develops dog-behaviour fully and uninterruptedly. Having done so, on the dissolution of the body, after death, he reappears in the company of dogs. But if he has such a view as this: 'By this virtue or observance or asceticism or holy life living like a dog, I shall become a great god or some lesser god: that is wrong view in his case. Now there are two destinations for one with wrong view, I say: hell or the animal realm. So, Punna, if his dog-duty succeeds, it will lead him to the company of dogs; if it fails, it will lead him to hell.”
When this was said, Seniya the naked dog-duty ascetic cried out and burst into tears"
—Majjhima Nikaya 57
" The ideal Cynic would evangelise; as the watchdog of humanity, they thought it was their duty to hound people about the error of their ways.[10] The example of the Cynic’s life (and the use of the Cynic’s biting satire) would dig up and expose the pretensions which lay at the root of everyday conventions.[10]"—Wikipedia