But in Japan (and many places) winter is poetically associated with death. (though I'm not an expert on Japanese poetry and it could be more complicated than that)
Also, the ending winter's effects seem to be continuing to this day, because Jahn, Aine, Idoun, and Fa all use dragon stones, yet it doesn't seem like Elibe is particularly cold besides the pegasus country (Ilia?). It would be weird if the ending winter in elibe was still going on primarily as a function of temperature, yet mostly more mild in nature than winter in our world. Ninian doesn't explicitly use a stone, but she and Nils, both ice dragons are also mostly in human form during the events of the game, rather than mostly draconic.