I can't speak for your specific drone, but I have experience with electronics and cold weather.
I would definitely store the batteries in the warm, and check the manufacturer's guidelines for the correct storage voltage (for a LiPo I think this is about 30% to 40% charge, or 3.85 volts per cell) It also doesn't hurt to store them in a fireproof container for extra safety.
The main hazard I've found when storing and operating electronics in freezing conditions is the risk of freeze-thaw cycles when the temperature is hovering around 0°C. Once it is cold, it's generally OK.
Additionally, if you do decide to use the aircraft during the winter take care when moving it from a cold, dry environment into a warm one - condensation will form and can cause damage or corrosion. Let it warm up thoroughly before use - if possible, seal it into a watertight bag or box before bringing it in to preserve the dry air around the drone, and wait for it to warm up before opening to minimise condensation.