Hi Rosehoward
I was on the JY trip to Iceland in March last year (not November but still winter). Yes, it can be bitterly cold and very windy but if you dress in layers and take a thick waterproof jacket, you'll be fine. They have a saying there "If you don't like the weather here, just wait five minutes" and it's absolutely true - you could get all four seasons in half an hour, it's really that changeable!
I would also recommend some thick gloves, a hat, sturdy walking boots (particularly if you are planning to do the 'Golden Circle' (which I'd recommend) and also some 'Yaktrax' or similar grippers because it can get really slippery underfoot. One thing to remember is that you'll be on and off the heated coach a lot, so wear layers that are easy to slip on and off. The hotel is also very warm and comfortable, so you don't have to come down to breakfast dressed like the Michelin man!
The plus side of the short days and dark skies is the possibility of seeing the Northern Lights. There are no promises of course but, if you get lucky as we did, it will be one of the highlights of your year.
Iceland is a wild and beautiful country with superb food and extremely friendly and welcoming locals. I'd really like to go back one day so I'd definitely recommend that you go for it and book.
Happy to answer any other questions
All the best
Mandy