Why did Augustine attempt to stop Christians from walking barefoot?

I think that Henry Chadwick is conflating Manichaeism with Christian asceticism, toward which he appears to have a bias. He clearly indicates in another work - Priscillian of Avila: The Occult and Charismatic in the Early Church - that he had Manichaeism in mind when he interpreted the passage, but also considered certain non-canonical Christian ritual ascetical practices. Georgetown Professor James O'Donnell observes (here), however, that although the latter troubled Augustine, he did not think it merited a severe rebuke, as he attests in his Letter No. 55:

I cannot, however, sanction with my approbation those ceremonies which are departures from the custom of the Church, and are instituted on the pretext of being symbolic of some holy mystery; although, for the sake of avoiding offense to the piety of some and the pugnacity of others, I do not venture to condemn severely many things of this kind. But this I deplore, and have too much occasion to do so, that comparatively little attention is paid to many of the most wholesome rites which Scripture has enjoined; and that so many false notions everywhere prevail, that more severe rebuke would be administered to a man who should touch the ground with his feet bare during the octaves (before his baptism), than to one who drowned his intellect in drunkenness. My opinion therefore is, that wherever it is possible, all those things should be abolished without hesitation, which neither have warrant in Holy Scripture, nor are found to have been appointed by councils of bishops, nor are confirmed by the practice of the universal Church, but are so infinitely various, according to the different customs of different places, that it is with difficulty, if at all, that the reasons which guided men in appointing them can be discovered (XIX.35)

I would submit, however, that although Augustine may have objected (mildly) to non-canonical ritual Christian ascetic practices, he did not object to Christian asceticism in general. This is evidenced in how he refers to the Egyptian monk, Antony (Anthony the Great), one of the strictest ascetics of his time:

A conversation ensued on his [Pontitianus, a Christian] speaking of Antony, the Egyptian monk, whose name was in high repute among Thy servants, though up to that time not familiar to us. When he came to know this, he lingered on that topic, imparting to us a knowledge of this man so eminent, and marvelling at our ignorance. But we were amazed, hearing Thy wonderful works most fully manifested in times so recent, and almost in our own, wrought in the true faith and the Catholic Church. We all wondered — we, that they were so great, and he, that we had never heard of them.

Confessions, Book VIII, XII.29

I think further evidence of a bias against Christian asceticism comes out in the way Chadwick chose to translate the Latin, fortissimo dominatori corporis, usque ad Italicum solum glaciale nudo pede obterendum insolito ausu (IX.VI.14). Chadwick's translation reads, as you cite:

... and tamed his body to a tough discipline of extraordinary boldness: he went barefoot on the icy soil of Italy.

By comparison, the translation in the Nicene and Post-Nicene Fathers edition of Confessions reads:

... being so brave a tamer of the body, as with unusual fortitude to tread the frozen soil of Italy with his naked feet.

Other translations:

... a most valiant tamer of the body, so as, with unwonted venture, to wear the frozen ground of Italy with his bare feet [Pusey].

... and was so brave a tamer of his body that he would walk the frozen Italian soil with his naked feet, which called for unusual fortitude [Outler]

Augustine attempted during his life to end not only certain ascetical practices associated with Manichaesm, but indeed the cult itself (to which he at one time belonged), as evidenced by the large corpus of work he wrote against it (e.g. On the Morals of the Manichaeans, Concerning Two Souls, Disputation against Fortunatus, Against the Epistle of Manichaeus Called Fundamental). This is not to say, however, that he condemned similar ascetical practices undertaken by Christians for entirely different purposes.

I would submit that the short passage cited, when translated appropriately, shows Augustine's support, rather than disdain, for Christian asceticism.

This apparent bias against Christian asceticism reflected in Chadwick's comment seems not to be unique. The editors of Augustine's Anti-Manichaean Writings in the Nicene and Post-Nicene Fathers series make the following statement, without any further elucidation or support, in their introduction:

Many Christians were in a position to be attracted strongly by the Manichæan theory and practice. The later asceticism as it appeared in the hermit life of the fourth and following centuries was essentially pagan and had much in common with the Manichæan.