Laudator Temporis Acti

Patrick Leigh Fermor (1915-2011), Mani: Travels in the Southern Peloponnese (London: John Murray, 1958; rpt. New York: New York Review Books, 2006), p. 23:

These empty peaks, according to Homer, were the haunt of Artemis and of three goat-footed nymphs who would engage lonely travellers in a country dance and lead them up unsuspectingly to the precipice where they tripped them up and sent them spinning down the gulf....

I can't find this anywhere in Homer. And are nymphs ever goat-footed?

Cf. Homer, Odyssey 6.102-109 (describing Nausicaa; tr. A.T. Murray and George E. Dimock):

And even as Artemis, the archer, roves over the mountains, along the ridges of lofty Taygetus or Erymanthus, joying in the pursuit of boars and swift deers, and the wood nymphs, daughters of Zeus who bears the aegis, share her sport, and Leto is glad at heart—high above them all Artemis holds her head and brows, and easily may she be known, though all are beautiful—so amid her handmaids shone the unwed maiden.

οἵη δ᾽ Ἄρτεμις εἶσι κατ᾽ οὔρεα ἰοχέαιρα,
ἢ κατὰ Τηΰγετον περιμήκετον ἢ Ἐρύμανθον,
τερπομένη κάπροισι καὶ ὠκείῃς ἐλάφοισι·
τῇ δέ θ᾽ ἅμα νύμφαι, κοῦραι Διὸς αἰγιόχοιο,        105
ἀγρονόμοι παίζουσι, γέγηθε δέ τε φρένα Λητώ·
πασάων δ᾽ ὑπὲρ ἥ γε κάρη ἔχει ἠδὲ μέτωπα,
ῥεῖά τ᾽ ἀριγνώτη πέλεται, καλαὶ δέ τε πᾶσαι·
ὣς ἥ γ᾽ ἀμφιπόλοισι μετέπρεπε παρθένος ἀδμής.

Cf. also Homeric Hymn 19.1-14 (tr. Hugh G. Evelyn-White):

Muse, tell me about Pan, the dear son of Hermes, with his goat's feet and two horns—a lover of merry noise. Through wooded glades he wanders with dancing nymphs who foot it on some sheer cliff's edge, calling upon Pan, the shepherd-god, long-haired, unkempt. He has every snowy crest and the mountain peaks and rocky crests for his domain; hither and thither he goes through the close thickets, now lured by soft streams, and now he presses on amongst towering crags and climbs up to the highest peak that overlooks the flocks. Often he courses through the glistening high mountains, and often on the shouldered hills he speeds along slaying wild beasts, this keen-eyed god.

ἀμφί μοι Ἑρμείαο φίλον γόνον ἔννεπε, Μοῦσα,
αἰγιπόδην, δικέρωτα, φιλόκροτον, ὅστ᾽ ἀνὰ πίση
δενδρήεντ᾽ ἄμυδις φοιτᾷ χορογηθέσι νύμφαις,
αἵ τε κατ᾽ αἰγίλιπος πέτρης στείβουσι κάρηνα
Πᾶν᾽ ἀνακεκλόμεναι, νόμιον θεόν, ἀγλαέθειρον,        5
αὐχμήενθ᾽, ὃς πάντα λόφον νιφόεντα λέλογχε
καὶ κορυφὰς ὀρέων καὶ πετρήεντα κάρηνα.
φοιτᾷ δ᾽ ἔνθα καὶ ἔνθα διὰ ῥωπήια πυκνά,
ἄλλοτε μὲν ῥείθροισιν ἐφελκόμενος μαλακοῖσιν,
ἄλλοτε δ᾽ αὖ πέτρῃσιν ἐν ἠλιβάτοισι διοιχνεῖ,        10
ἀκροτάτην κορυφὴν μηλοσκόπον εἰσαναβαίνων.
πολλάκι δ᾽ ἀργινόεντα διέδραμεν οὔρεα μακρά,
πολλάκι δ᾽ ἐν κνημοῖσι διήλασε θῆρας ἐναίρων,
ὀξέα δερκόμενος.

In later classical literature, on Crete, Amaltheia sometimes appears as a nymph, sometimes as a goat: see Jennifer Larson, Greek Nymphs: Myth, Cult, Lore (Oxford: Oxford University Press, 2001), p. 317, n. 224.

I wonder if Fermor may have conflated Odyssey 6.102-109 with some modern folk tale. See John Cuthbert Lawson, Modern Greek Folklore and Ancient Greek Religion: A Study in Survivals (Cambridge: Cambridge University Press, 1910), p. 133:

Only in one particular is the beauty of the Nereids ever thought to be marred; in some localities they are said to have the feet of goats or of asses²; as for instance the three Nereids who are believed to dance together without pause on the heights of Taÿgetus. But this is a somewhat rare and local trait, and must have been transferred to them, it would seem, from Pan and his attendant satyrs, with whom of old they were wont to consort; in general they are held to be of beauty unblemished.

² Cf. Bern. Schmidt, Das Volksleben, p. 105.