Hi Debbie,
This certainly sounds like an odd problem. If your veterinarian has not found any medical conditions, then behavioral seems possible. It could be that there is something along the walking routes that is disconcerting to him and this could be a fear type response, particularly if the action is the same in the same location repeatedly. Alternatively, we could look at the various factors including weather but also the apparatus he is being walked on (collar, harness, halter). Working on positive reinforcement while getting him to do what you want is likely the best way to start. If concerned about this behavior, it might be best to meet up with a certified dog behaviorist or trainer in your area to have them along on a series of walks to witness the concern first hand.
All the best.
Dr. Ryan Llera