You know you, and you know your priorities. IMO cold is less critical than grey: there are cold places where there is plenty of sunshine, and other places that are cold and grey (NW PA comes to mind). Bright skies can make up for a lot!
In general, I would put cold behind most metrics in terms of importance. Academics and the overall campus culture would be the two biggest to me, closely followed by 'extra’s (ECs, on & off campus activities). Dorms and food would come next, followed by weather and travel access. BUT: that’s me. When you think about why you are choosing to go to BS, what are the most important factors to you & your family?