Here in Michigan, the state mandates a specific number of hours (1,098 hours) and days (180 days) students must be in school.
To count as an "instructional day", district wide attendance must be 75%.
If a district expects more than 25% of their students are going to stay home because of the weather, they may as well call a snow day because they'll be making that day up at the end of the year anyway. A limited number of snow days are "forgiven" and not required to be made up at the end of the year.
In my particular neck of the woods, there is generally broad agreement by superintendents from different districts to call snow days at the same time. Some schools don't have any bussing and weather tends to affect their attendance more than districts that do. If a non-bussing district calls for a snow day, parents from neighboring districts (that maybe do have bussing) will often choose to keep their kids home: "Why does my child's district care less about safety than other districts? If it's bad enough for a district 3 miles away to call a snow day, I'm keeping my child home too." This can create a situation where even open districts fall below that 75% threshold.
NWS reports are also provide a lot of guidance. A warning of any type (winter storm warning, wind chill warning, ice storm warning) will almost always result in no school. Other weather advisories really depend on situation.
Source: My wife is an elementary teacher (and loves snow days as much as her students).