"The days are short in the winter."
Translation:Kışın günler kısadır.
Kışın = in winter :-)
With kış (winter) and yaz (summer), the locative case is irregular for some reason. So it's not actually a genitive ('possessor') case ending, it just happens to look the same! And that's why "kışta" isn't accepted here. Another Duo example:
Kışın mutsuzum, yazın mutluyum. = In the winter I am unhappy, in the summer I am happy. here
As for "Kışın günleri", (possessive) that would just have a slightly different translation: "the days OF winter", rather than "the days IN winter" :-)