About 18 years ago I had to carry an 80 lb dog 50 yards across a snow covered plowed field in blizzard conditions with a -30F wind chill. His legs had gotten too cold and he just laid down. The experience made an impression on me.
We put boots on the dogs when the actual air temps get below about 0F and there is little or no snow. Much snow depth causes a problem for the booties though as they get pulled off, or cause the dog more trouble than they're worth, so we just stay close and watch closely for signs of distress when there is a lot of snow.
Finally, we have a dog rescue sled set up in case one gets immobilized out there in the snow. I doubt I could repeat my feat of 2 decades ago, and I know my wife couldn't.