We do not find the weather in the northeast of the US depressing. Living in the Northeast (not too far from the schools that you mentioned) both daughters nonetheless stayed in this area or went even further north for university.
One issue is that we are used to it. Another issue is that we ski. In general however people find activities that are conducive to the climate, whether this means skiing or skating or means indoor activities in the winter.
I think that you will get used to it reasonably quickly.