There are some ways that you can make going out into the cold more comfortable for your puppy and help train your Boxer to go outside in the cold for housebreaking:
Put a canine sweater, vest or coat on your puppy. Some Boxers need clothes, and specifically a coat or vest
that helps the dog maintain core body temperature. In the winter, most will do well with a water-resistant fabric.
When your Boxer is led outside with an outer layer of protection, and realizes that the cold air is not biting at him, he will be more prone to actually enjoy being outside, exploring around a bit and relieving himself.
2) Protect the paws. A dog's paw is made of skin. While it is thick skin, it is still skin. It is a very huge misconception that a dog's paw can handle any surfaces. When it's really cold out, the ground is even colder than the air. And this will be transferred to a puppy or dog's paws. It can end up really chilling a dog.
You can use a quality paw wax, which has the added benefit of keeping the paws moisturized, protected from ice and 'snowballing' (when tiny pieces of ice or snow get stuck between the toes or between paw pads) and will offer a dog better traction in what can be slippery surfaces.
If your Boxer has very dry paws, you will want to use a paw balm that heals dry skin.
Another option, but one that only some dogs tolerate (Boxers seem to either love it or hate it) are canine shoes. If you do opt for this, look for those that close around the ankle with velcro, as these are very easy to get on and off.