When it comes to winter cycling, I'm a sunshine patriot. Few things are more miserable than riding in the rain or snow, or contaminated/dirty road surfaces, let alone when it's cold. I don't mind the cold if it's dry out, I'll dress for it and enjoy the ride. So I am no expert on this question... but I'll share my experience.
Riding in rain or on contaminated roads (water, slush, dust, dirt, etc.) is very hard on the drivetrain and greatly accelerates wear of chain & sprockets. Can also accelerate wear of rims, brake pads, rotors. No matter how you lube, wet (oil) or dry (wax), you'll be cleaning and re-lubing much more often, sometimes after every ride. And if you're doing that, it doesn't matter much what kind of lube you use.