So far I've always managed to have the greenhouse by winter. So there isn't much difference with the other seasons, except I move my sprinklers into the greenhouse.
Other than that, it's the same as any other season. Farm, mine, fish, forage, kill things and make friends.
I tend to gather a lot of wood and stone and have Robin build things in winter, too.
I tend to leave GI for winter, too, because that way I don't have crops to manage and my animals should have an autofeeder. So I can just spend the winter there, like the SV version of Ibiza (or Cancun if you're on the other side of the pond).