I expected some reference so some country's lore where foxes did that, but the real explanation is actually much nicer.
The sexual theme is so common that 狐狸精 "fox spirit" became a term of abuse for overly sexual women. Chinese people like to translate the term into English as "vixen".
Since Zelda is a Nintendo game and Ghost of Tsushima is set in Japan, I would think it has more to do with real world lore than a reference to Skyrim.
I don't remember any significant dogs in Kakariko Village (where the windmill was), or the ability to give food to any of them.