Originally Posted by
Driver8
It's your life and your hike, but I would consider the SOBO from Gorham, with the following internal flip-flop: start in Hanover, which gives you an easily reached start town and some relatively easy trail to warm up on the first few days, addressing your concern about a cold start, then continue on to Gorham. Hitch a ride of some sort back to Hanover - there's lots of resources available for such a ride, just look around here. Work south from there - after the Whites, the rest will be cake. I'd suggest that, one you get to Glencliff, slacking from Kinsman Notch back to Hikers Welcome hostel might make sense rather than descending Beaver Brook Trail, but that's your call. (Lots of thrus do that, so you could probably share that ride with some late-season thrus and split the cost.)
Chet's Place is a friendly and helpful hostel in Lincoln - I recommend from many stays there.
Anyhow, do what you like, just understand that an October traverse of the A.T. in the Whites is a big one to bite off and try to chew. The Whites are HARD. Hard in mid-summer. Much harder than most all of the trail south of them, though there are spots which briefly approximate some elements of the difficulty they present, though few that capture them all, from everything I read and and hear and from my somewhat limited experience - I haven't hit much of New York yet, nothing south of it on the A.T. But I trust when a lot of smart and experienced hikers here tell me and I read their accounts that the trail south of New England is much smoother than what you see in New Hampshire and much of Maine. All that glacial scouring over rock. Vermont Long Trail north of the A.T. split at Route 4 will present similar challenges and issues to the Whites, by the way, from everything I hear and, so that's not an "easy" alternative.
Again, your life, your hike, your money, etc., but in your shoes, I'd be strongly inclined to spend a day or two of travel and a couple hundred bucks to ensure a much more agreeable, enjoyable hike, most likely - there are few if any guarantees backpacking in the White Mountains.