I don't believe that the timescale in the game is meant to be taken literally, as it probably would've been really tedious to actually make the in-game year 365 days. In my headcanon, spring is March, April, and May, summer is June, July, and August, fall is September, October, and November, and winter is December, January, and February. Adding onto this, it would also mean that that Stardew world's version of the new year is instead marked by the end of winter and beginning of spring. Not only that, but with the Feast of the Winter Star presumably taking place in February if this is true, it's likely a celebration of the coming spring.