Hi
I'm in the UK and have numerous broody hens, some very reliable ones, but I've never had one go broody in the winter yet. A couple of years ago my most reliable broody and her daughter had amassed a mountain of 47 eggs (all still edible thankfully) in a secret nest which I found the day after Boxing Day and neither of them showed any interest in brooding them....just kept climbing up the pile and dropping another one on the top! They had obviously been laying in there for several weeks, so in general I would say it would be unlikely for your hen to go broody now, even if you leave her a nest of eggs, but nothing is impossible. The thing I love about my broody hens is that they take time off laying during the summer when I have plenty of eggs, to raise chicks and then lay in the winter when many of the layers are having time off.
Good luck with her and I hope she is one of the exceptions that does winter brood.