Yes. Absolutely. Winter lasts a looooong time up North. It snowed last week. Spring Term is really a misnomer, it should be called Second Winter term until early May.
If your kid is passionate about a specific spring sport, then a NE boarding school might be tricky. Maybe check the requirements for spring activities to make sure that the school isn’t going to be making your kid go out and break the ice on the water before crew practice. If you’re allowed to choose performing arts, debate, robotics or something more ‘indoor’ then that might help.