I tell people to get as much as they can out of worn components for winter riding. As long as you can handle the slop in shifting, and that first ride where you're actually skipping in either certain cogs out back and/or the middle ring, go for it -- hold off on the replacement stuff as long as you can or until Spring, whichever comes first. I work in a shop in York ME, and a guy just asked me this about his drivetrain -- while it was marginal, he can still get a lot of wear out of it, convinced him to ride it through the Winter.
But if you do have to swap out in the middle of Winter, consider cheap components for winter use only, and then swap them out for the nicer stuff in the Spring See if there's a 105 or Tiagra chainring that would work, same level for chain and cass. If there's still wear left in them, save them for the next winter and/or emergency spares.