Only when there is a hugely long winter should there be a main popup window and the event chains start coming.
I mean winters normal for those living in the affected areas, no big deal to them. So yeah if you are notified there that seasons are starting and ending then it wouldn't be too intrusive a thing. You should probably be informed that the 'seasons are changing' via the inbox at the top right (not opened game in a while, so I can't remember what they call that lol). Seasons change fairly regularly if you think over the long period of playing the game, therefore I don't think there should be pop up windows to inform you winter has started/ended. Just giving it a quick thought, this is how I would imagine it working in game for me.
