Harry hadn't planned ahead to bring something to help her keep warm. To be fair, she probably wouldn't have accepted it anyway. So he just did his best not to notice, or at least to comment, on how cold she must've been in that dress.
The question of where they were going seemed to catch him off guard. "Well, New York City's closest. We could get back to Chicago, but nothing's really like home there, that I could tell. I've got a place in the city, or you can head to a hotel. If you check your pockets, you'll have a new wallet. Probably some cash. That's your new life, here." Harry knew that wasn't going to settle well, especially with the cop side of her, but he didn't really have a good explanation for it.