I'm a moderately intelligent individual and it's taken me 43 years to figure this one out - scary, I know. It's really a good idea to shut your blinds or curtains or whatever window coverings you have and not for the obvious reasons.
Here's the deal. Our house backs up to a park, so we have no neighbors behind us, but we have many very large banks of windows to enjoy the beautiful view. This is all very good and fine. Because we don't have anyone wandering through the park after dark in the dead of winter, we frequently left the back blinds open all the time. You know, why go through the work of shutting them at night only to have to open them again in the morning!
Well, I'll tell you why. Apparently shutting the blinds saves money - at least in MN in the middle of winter. For whatever reason I started shutting the blinds at night this winter and I have discovered through reading our heating bill, that we are using less energy to heat our home this year than we did last year. All this despite the average temperature being lower this year than last year. So, it's colder outside, but we are using less energy to maintain that balmy 68 degrees inside (that's during the day, at night we hover at 60 degrees).
Now, most of you probably shut your curtains for privacy reasons anyway, but if by chance you are leaving them open and you live in the frozen tundra, shut the blinds!