Yes, apple cider can ferment in the fridge, but it does so at a glacial pace. Your refrigerator is set to around 38-40°F (3-4°C), which is like sending the yeast cells into a deep hibernation. They’re still alive, just really, really sleepy.
Think of it like a sloth on a lazy Sunday afternoon. The cold slows down their metabolism so much that it might take weeks or even months for any noticeable fizz to appear. So no, you won’t open your door one morning to find a bubbling cider volcano—thank goodness!