Why don't anime/manga girls usually wear winter hats? I perhaps understand why they don't bother with hats at Tokyo since it's fairly far south and at sea level, so a "cold" winter day in Tokyo is usually barely below zero Celsius/Centigrade, but the "Non Nons" live up in the mountains where they seem to get full winter for at least two months a year so it's gotta be approaching zero Fahrenheit.
While I know Asahigaoka village has elements of small towns from all over Japan, my best guess for where Asahigaoka would most likely be (if it existed, which it doesn't) is somewhere in northern Chūbu, since it gets a decent amount of snow in winter but it's not likely in Tōhoku or Hokkaido since the closest city (which I generally think of as a city like Niigata or Tōyama) is far south enough that oranges grow on trees near the station. Although neither of those cities completely fit either since Hikage claims it takes roughly 6 hours to get there from Tokyo by Shinkansen and neither of those cities take more than around two and a half hours to get to on the Shinkansen (unless Hikage's also including the amount of time it takes her to get to Asahigaoka on smaller, slower train lines from wherever she gets off the Shinkansen).