I suspect the answer, as it often is, is "it depends." I don't (usually) ride in ice or snow, so I don't worry about traction. (After all, our snow removal plan is best described as "wait until it melts!)
What's left? Rain, puddles, no street cleaning so broken glass, etc., and leaves collect on the roads and shoulders. Good summer tires aren't so great when there's lots of things to cause flats on the roads, particularly when the tires are worn from a summer of riding. My ideal would be to wear tires out around the first of December and replace them. While I'm changing tires from December through March, I'll often go to a more flat-resistant, heavier tire. But I'm too cheap to swap tires that aren't worn out. Now when May comes, I'll often look for the lightest tires in my stock to go on the bike.