This thread has been filled with good advice. Maybe it was the Greeks who gave us "Know thyself" but it's VFTT that gives us "Know thydog." It is very good advice to work up gradually. It on the one hand enables the dog to adapt and it enables the owner to know how the dog is reacting.
Sabrina's comments on the preliminary signs of being cold were spot on. I just purchased a new soft shell jacket for Lauky. It's a classic design. A very good outer shell with a light fleece on the inside and it zips up snugly. It looks like a Northface softshell jacket. He has been using a double layer fleece jacket. Yesterday was our first time with the new jacket and I decided to go with just that to start with. Temperature was about 15*. After about two hours he started lifting a paw, dropping his tail, rubbing his face in the snow as if burrowing and sitting. I could see he was getting cold. I stopped shortly after that to change water bottles and he started to shiver. Stopping, as has been mentioned before is also hard on dogs when it's cold. I quickly took off his jacket, put on the fleece jacket then put on the soft shell. Layering can work for dogs too. We got going again and he very quickly warmed up. His tail went up, he stopped shivering and even handled a brief stop at the summit with no problem. That was just an experiment yesterday. From now on when it's in the 20s or lower we'll just go with both of the jackets on.
Lauky's coat will continue to grow and thicken throughout the winter he handles the cold better as the winter goes on. But the key rules mentioned above are important. Work up gradually. Know your dog. Have everything you need to keep him warm. Be ready to turn back and quickly if your dog is getting cold.
I also agree that a dog's claws are important on ice. For that reason I carry booties in case of injury but tend not to use them.
The statement about the size of the dog is also spot on. My Airedale Duffy with the same type of coat as Lauky (Welsh Terrier) never got cold, but he was three times as big. He also had more difficulty hiking in hot weather than Lauky.
Be sensitive to your dog's needs. Remember he'll follow you anywhere so be ready to lead him back to the car if necessary. And happy hiking.
PS Handle that name Boone with care...It's a good one.