Boston Terriers have short hair, which makes them more susceptible to the cold. For a winter walk, wrap your dog up in a coat to protect them from adverse conditions.
Boston Terriers need less exercise than some other dogs, so on very cold days keep the walks shorter. They do still need exercise though, so be sure to take them out. Supplement the walks by playing with them indoors. Boston Terriers love games, so this will keep them healthy.
You also need to be careful with your Boston Terrier in warm weather. Due to their short snouts, the breed struggles to regulate their body temperature. The small airways make it difficult for them to pant out excess heat. Keep them cooler, and give them lots of water.
Plan your Boston Terriers walks around the day. In winter, head out at midday when the sun will be highest. In summer, stick to the cooler mornings and evenings.