Bar Harbor is where the Atlantic Coast ACA route ends up, right? You could just follow that from Bar Harbor to Boston.
As for the cold, it's doubtful you'd run into much snow, you'd just have to bundle up as much as possible on the bike. I'd still recommend against it though. Biking is going to work up a sweat, so then you're going to get too hot, then as soon as you stop biking the sweat's going to chill you to the BONE. In survival situations in cold climates the #1 rule is don't exert yourself to a sweat, for that precise reason.