One advantage is that private campgrounds would tend to be less expensive in the autumn. I passed through New England in August, and the prices were sky high because it was still high season. They were just about to drop, however.
About campgrounds on the Northern Tier, the ACA says, "Some cyclists may want to do the eastern portions of this route during the colors of autumn. If you do, call ahead to verify campgrounds because many close after Labor Day."
As far as weather in New England, use Rochester, VT (on the NT route) as an example. In October 2012, the high for the month was 76, low was 24. Average high was 60, average low was 40. There was no snow there in October 2012, but they got 3 inches in October 2011 (all in one day). Of course, 2011 in New England was a year of record precipitation. It sounds doable to me.
About the Green Mountains Loop in Vermont, the ACA says, "Generally, the cycling season in the region can be extended into mid October as long as you're prepared for cool, crisp mornings and brisk evenings."
I did the NT in 9 weeks, but I had the benefit of long days. Up north, the days before the equinox are longer than down south, but the days after the equinox are shorter. By the end of October, there's only 10 hours between sunrise and sunset in Bar Harbor.