Consider dog boots or balloon boots for your dog on cold and wet days. Especially when there's the chance if encountering salt on your walk. There will be days that it's cold and your dog won't require them. They have been walking without them for most of the year. If you're unsure then put them on. The waxy cream is also a good method to help your dogs feet from the cols and salt.
As far as coats go short breed dogs like Dalmatians, pointers, Jack Russell's, pugs, bulldogs, Staffordshire terriers etc usually require a coat. Dogs that usually do not and can be too warm are shepherds, collies, labs, goldens, Bernese Mountain Dogs etc.
If your dog is shaking it needs a coat. If it's panting it doesn't. If it's lifting it's paws frequently it needs boots. With the right help you can exercise them as much as you would on a milder day.