Time in school that is lost for student because of cancelled school days during winter storms should be made up in the beginning of summer. This is because there is a significant correlation between missed school days and children's performance on standardized tests. Furthermore, many of the countrys where students outperform those in the US have school during the summer anyways.
We are at a point in society where technology has advanced to the point where kid's can do their studies online at home. This really wasn't possible ten years ago but with the advancement's in technology and more people having computers than in the past it is. Plus its seems that the schools all work off of I-Pads anyways so I see no reason why they can't just do their studies at home.
If winter weather closes schools than they should us days already in the schedule such as in service days to make it up. Teachers deserve to have a summer holiday and should not have to baby sit over it. There are plenty of days already in the schedule to make them up already.
Unpredictable weather and municipal inability to cope are factors that are out of students' control. Snow days are built into the schedule to compensate for relatively short school closings (in some districts, 2-3 days per school year). Longer closings should not result in a shorter summer for students and should be dealt with in other ways.