My wife and I hiked up to stay at the Carter Notch Hut in October once the full-service season was over. It's a lot cheaper but you need to pack all your own food and bedding. We stayed on a Friday night and were the only guests, save for the 20-something caretaker who was a very nice guy.
If you are an adventurous sort and don't mind preparing your food and sleeping in an unheated bunkhouse, you'll love the huts in the off-season! From what I could tell, Saturdays are often still busy but if you go during the week you may have the whole place to yourself. Bankhouse/hut was clean and kitchen was awesome. Highly recommended.