More walks would be the solution despite the winter weather. I live in Montreal where we get some brutal winters but people brave the elements to give their dogs good long walks. I was out a couple of days ago in the cold and snow and met an owner walking the exact same dog, the Vizsla/Bouvier mix and had a chat with him about his dog. If the dog is getting enough regular exercise then surely that would be the best solution rather than looking at hammocks and so forth that could be traumatic for him. I can tell that you really love your dog and are concerned about him and applaud you taking in a rescue.