Not mandatorily. Kids look forward to summer break and should be able to enjoy their time off from school. Any lost time due to winter and snow days can be done during the school year. Students should be able to take home any lessons to be covered in case of school closures which, I think, should be easy nowadays with most everyone having easy access to computers. This should be the school's responsibility to ensure that. Summer school should only be for kids who are lagging behind or for those who choose to take advance classes.
Too bad you haven't gotten any replies, probably because it was posted in the wrong forum category. I have filed a request to have it moved to the Education & Science forum, hopefully that will make a difference.
Where I live, if you miss a day of school during the year because of snow or other weather conditions (my kids used to have hurricane days when we lived in Florida), the missed day(s) are tacked onto the end of the school year. I doubt anyone is proposing that kids attend school all summer because they missed a few days during the year.