Gotham is almost exclusively depicted as this very dark and gloomy city, and even winter holidays bring no joy to its citizens that are being constantly terrorized by a bunch of maniacs. This kind of atmosphere perfectly fits the series of games about Batman.
Of all other games in the DC lineup, Arkham Origins has one of the most fascinating winters. This was possible due to the APEX Turbulence technology, that allows some truly innovative weather effects, especially snow, to be created.
Although, Origins is considered to be the weakest game in the Arkham series, it is still pretty solid, so give it a go.