Killington is generally open well into April. They have made it to May in the past, though they closed for the season in late April last year, supposedly with enough snow left to keep operating. I didn't see it so I can't say, but they have been very aggressive in trying to open early and close late in the past (I remember riding in trailers pulled by 4x4's to get to the lowest open lift on opening day about 15 years ago).
There will probably be a few ski areas open in this part of the country in April, but you shouldn't expect anything like the conditions you would get in the middle of the winter. In Utah spring skiing means soft snow and tons of trails to choose from. In the eastern US it would have to be an exceptional season for any mountain to have more than a handful of runs open by the middle of April.
That said, the skiing in New England is great right now
