There are a number of different breeds of dogs that simply aren't winter dogs. This doesn't mean that they are not wonderful house pets even in very cold climates, but it does mean that potential owners or current owners have to take into consideration the cold intolerance of these dogs.
Dogs have been bred by man for centuries and literally hundreds of dog generations to have specific types of characteristics. These characteristics are not always the same traits that the wild wolves, primitive dog types and the hardy, outdoors types of dogs have been bred for. In a very basic sense man has almost gone against nature in creating some of these breeds, and so owners need to recognize that there is nothing they can do to toughen up or make these breeds cold tolerant.
There are some breeds that are obviously cold intolerant. These tend to be the tiny toy breeds as well as the very short haired breeds. Of course most people are aware that the Chihuahua, especially the short coated variety, is very sensitive to even cool temperatures. Temperatures in the low sixties and high fifties can even result in shivering, and anything below about 40 degrees Fahrenheit is really difficult for these dogs to tolerate even for a few minutes. Longer haired Chihuahuas are a bit more hardy but also not cold tolerant.
Other dogs that are simply not good in the cold include the Whippet, Italian Greyhound, Saluki and the Greyhound. These dogs aren't ideally equipped for cold weather for two very important reasons. The first is their noticeably fine and vey short coat that offers little in the way of insulation or protection from the cold air. The second reason is that these are racing breeds, built to be lean and have very little body fat. This means that there is no internal insulation either. These breeds will have much more dramatic changes in body core temperatures in even slightly colder weather conditions than other short coated dogs with a good layer of internal body fat. Often the cooler above freezing temperatures are even problematic for these breeds and cold mixed with damp can be deadly in a very short period of time unless the dog is suitably dressed for the weather and protected from the cold and damp.
The dogs that have been bred and developed in very warm climates such as South Africa, Egypt and the Middle Eastern countries may also be less ideally suited to cold weather for ever short periods of time. The Basenji, Pharaoh and Ibizan Hounds are not recommended for more than the necessary restroom breaks outside, however they aren't adverse to being outdoors. Often with a coat or sweater these dogs love to get out and play in the snow, and they can tolerate above freezing temperatures even with snow provided they are able to stay dry. If they do get wet with melting snow or falling snow, they will need to be brought in and thoroughly dried to prevent possible issues with hypothermia and chilling.
There are other shorter haired breeds that are similar to the dog's mentioned above that love to be outdoors even in the winter but are not considered to be cold tolerant. These dogs do great for a walk, run or playtime outdoors, immediately followed by being brought inside to warm up and dry off. These breeds all typically have shorter hair, but they also have good body insulation in the form of a layer of fat under the skin and around the body core organs that provides additional heat retention and insulation.
These breeds include the Great Dane, German Shorthaired Pointers, Bassett Hounds, Bloodhounds, Boxers, Dachshunds, Vizsla, Beagles, Pugs, Bulldogs, Yorkshire Terriers, Maltese and the Rhodesian Ridgeback. Remember that these dogs will love to be outdoors with you, at least most of them will, and they typically will stay outdoors in the snow and cold as long as you are outside to be with them and play. It is therefore important to monitor your dog and bring them in before they become chilled. If you are playing with them and they are running around, bring them in before they are allowed to stand outside to cool off. This can actually cause a chilling effect that can dramatically drop the internal temperature and possibly cause mild hypothermia in a very short period of time.
The American Pit Bull, Chinese Shar-Pei, Shih Tzu, Papillon and the Havanese can also fit into this same category, although some of these dogs are more moderately cold tolerant. Moving to dogs that are less cold intolerant but still not appropriate for longer periods of time outside in cold winter weather causes the list to get even longer.
Perhaps not surprisingly these dogs are more often the short haired breeds, but they also include many of the single coat long haired large sized dogs as well. The Setters tend to fit into this category, loving to be outside running and playing in the snow and cold but not able to tolerate being cold and wet or left in cold conditions for longer periods of time. The Standard Poodle, if clipped is considered to have little tolerance for the cold, but if the coat is left longer and natural they are moderately cold intolerant. Toy Poodles and the so called teacup, micro or mini sizes are in the highly intolerant to cold category.
Remember that in areas where there is a higher amount of snow, smaller dogs are going to have more problems with remaining out of the snow when moving around than dog's with longer legs. When the snow is constantly around the dog or being blown into the dog from the ground, they are going to become colder than a dog that is above this snow level. In addition, moving through the snow is going to be more difficult, resulting in a great expenditure, increased body temperature and a greater risk of fast cool down when the dog stops moving.