Wow, such a snowy bike! Bike will be need to clean for a long time after the ride ... and during the ride. But what do if chain will freeze during the ride?
The chain is not the main problem. I have in winter always a spray can with penetrating-oil in the backpack. :-) A big problem is humidity in the wheel hub. Then the pawl elements of the free-wheeling are freezing up! A power transmission from the chain to the rear wheel is then not possible any more. It helps only, to lubricate the hub with nonhardening-oil beforehand and to renew the hub's seals on occasion!