It's not unusual to see dogs wearing sweaters or coats in winter, but for most canines, especially big dogs, outerwear is unnecessary: they have plenty of undercoat and fur to keep them warm. However, under some circumstances it's worthwhile for a pooch to sport a sweater.
Smaller dogs may have more difficulty generating and retaining body heat, so they're good candidates for sweaters or coats that not only protect them from the elements but also provide warmth. Breeds like short-haired Chihuahuas, pugs and Yorkies -- who have long hair but not thick undercoats -- can benefit from wearing protection in cold weather whether it's fashionable or not.
Older or chronically ill pups will benefit from wearing sweaters and coats. The warmth of protective outer wear will help dogs with arthritis or other types of joint pain feel better; Such dogs need more care than simply covering with a coat, but a covering nonetheless will be of some benefit. Dogs with circulation problems may be naturally cold; sweaters will help them to stay warm, promoting circulation.
Dogs with thin body types and those with very short fur also do well with sweaters and coats. Racing dogs like whippets and greyhounds naturally get cold easily, and their thin skin can get scraped, nicked and torn easily. Protective wear is a plus.