Can you walk to the local train station from Brewster Hill?

I wouldn't suggest it either. Brewster Village is really the only "walkable" part of the area. It's also not that close. I think Brewster Hill is probably closer to the Southeast station, but from my experience parking was easier at the Brewster station.

It's a moderate walk that's mostly downhill, just beware because there aren't sidewalks until you get closer to the Village. I wouldn't suggest walking from the train station to Brewster Hill.