In a situation like today, the only way to play it safe is to call it off ahead of time.
Let's say they come in to school normal time, and realize around 11:30 that the snow is starting to come down hard. At that point they have to scramble around to make calls to the bus company, try to get them out there in time before the snow builds up even more. Parents that provide transportation their kids now have to be notified and hope they can get down there.
Classes are cut short and the whole schedule gets screwed up. Unlike a planned half day when all the times are adjusted accordingly, they can't be for an early release because of snow. Also, an early dismissal before a certain time in the school day doesn't count as a full day, so they would still have to make it up in the summer. Sometimes they wait it out to make a half day and then they don't have to make it up in the summer.
In our district, we even have students coming from surrounding towns sometimes due to special needs. They have vans drive them to and from.
I know here in Plainville it started to hit around noon and came down fast. I'm not sure about East Hartford because I called outta work. School was closed, but not a district closing and I'm one of the lucky few that gets to come in when schools are closed.

There was no way I was going to get up, head over to an empty school, hang out for a few hours and then be dismissed early and battle the traffic on I-84.