The important quotation is
the bridle of a horse: aureas dicebant frenos, quibus equorum aures religantur, Paul. ex Fest. p. 27 Müll.
"They call the reins aureas, with which the ears of horses are bound up."
In the third section of Ainsworth's lexicon, Index Vocum (Dialects) 'aureas' is explained as both a dialect adjective meaning 'of the ears,' a head-stall, and hence by synecdoche 'the bridle itself.'
[ qu. orea, frequens enim est commutatio o in au, ap. ant. quod fit in oro equi, ...] and then gives an example from Greek.
Finally he mentions Aureax [ cf auriger] a carter. But these are all late or dialect forms.