Paraffin oil is mineral oil. It's just a simple alkane. Mineral oil from the drugstore is the cleanest purest variety. Petroleum jelly - Vaseline - is the same thing. Simple alkanes. Paraffin wax is a long chain simple alkane. Short chain is liquid, long chain is solid.
Wax doesn't work in cold and doesn't work well under heavy load. When someone tells you wax lasts a l-o-o-o-o-ng time mostly it's because they don't ride that hard. The shop selling the prepped and waxed 'racing chain' will tell you one hard ride.
NFS chainlube. 12 drops does a complete chain. Really. The disbelief is the reason they can't sell much. I add one or two drops every hundred miles. If using the bike in brine yes more maintenance is required on every part of the bike. But not so much for the chain. Currently I no longer ride at -20 Fahrenheit but I have. I can tell you NFS works quite well at -5. If heavily brined maybe add two drops per hour the bike was outside. Add the oil just before you head out so that it spreads around. If you just have to add oil before parking it run the cranks backwards a dozen times . That's all that is required. Could not be simpler.
When it's super cold it's more like short dashes on the bike than long rides anyway. In years past used to bring the bike in with 20 and 30 pounds of ice all over everything. Never much worried about the chain. Getting clothes clean and coping with the flood on the floor was the hard part.