According to Minnesota State laws the temperature would have to get to -30 F degrees which is very cold before the schools in Minnesota would be forced to close.
Any warmer than that then the schools will likely be in session unless the roads get very dangerous to travel on.
Schools have heaters to keep the school warm so unless it gets really cold as in below freezing or heavy snow or ice then it's likely that the school will still be open and in session even on a cold day.