The dogs of Kerfol (Kerfol)
The dogs are ordered chronologically by their appearances in the 17th century Kerfol.
The first dog
Although the breed is not stated by Wharton, she describes the dog really precisely. The dog is "[…] Chinese, and that he was of a rare variety called the "Sleeve-dog." He was very small and golden brown, with large brown eyes and a ruffled throat: he looked rather like a large tawny chrysanthemum." [1]
There is only one breed that fits the description precisely, which is the Pekingese.
Pekingese
https://en.wikipedia.org/wiki/Pekingese#/media/File:Peki%C5%84czyk_f64.jpg
The Pekingese belongs to the toy dog breed and was developed in ancient China. It was kept by the imperial family as palace dogs and considered to be sacred. In 1860, English soldiers looted the Palace of Peking and found these dogs there; since then they are also known in the West. Pekingese are about 15-23 cm tall and weigh roughly 6.5 kg. Due to its full mane, the Pekingese is also known as "lion dog." Chinese royalty carried the dogs in the sleeves of their robes, which created the term "sleeve dogs." While the coat can vary in its color, the face is always characterized by a black mask.[2]
It's worth mentioning that Edith Wharton owned two prized Pekingese.[3]
The second dog
Again, the breed of the dog is unknown, but this time it's only described vaguely. It's "[…] a white dog with a feathery coat and one blue and one brown eye."[4]
The information provided is not enough to define that dog, but as an example of the feathered coat; here is a picture of a Cocker Spaniel. I highly suppose the dog being a Cocker Spaniel, due to the fact, that Edith Wharton had a weakness for toy dogs.
American Cocker Spaniel
https://en.wikipedia.org/wiki/Cocker_Spaniel#/media/File:Jakestacksmudgename.jpg
The third dog
This time Wharton declares the breed of the dog "[…] one bitter cold evening a poor lean greyhound was found whining at the castle-gate […]"[5]
A racing Greyhound at full extension
https://en.wikipedia.org/wiki/Greyhound#/media/File:Greyhound_Racing_2_amk.jpg
The greyhound is one of the oldest dog breeds and was developed nearly 5,000 years ago in ancient Egypt. In England they were known by the 9th century and were bred especially by the aristocracy. For the common folk, it was actually illegal to own a greyhound for about 700 years. Greyhounds were mostly used for hunting and dog races. Its height is about 66 cm and the weight approximately around 29.5 kg.[6]
The fourth dog
The fourth dog is a mongrel of unknown breed. The only information provided is that "[…] a long-haired white mongre,l slipped out of a doorway and joined the others" [7] and that "[…] she found a young sheep-dog, a brindled puppy with good blue eyes, lying with a broken leg in the snow of the park."[8]
Sheepdog stands for a category of a dog breed and not for a breed itself. Since it's a mongrel, it's even harder to tell what kind of dog that is. The height of most sheepdog is roughly 60 cm and the weight over 50kg. Sheepdogs were developed to help to herd sheep.[9]
An example of that breed would be the Border Collie.
Male Border Collie
The fifth dog
The last dog of the story is a pointer. "[…] a large white pointer with one brown ear. He was an old grave dog, much more experienced than the others; and he seemed to be observing me with a deeper intentness."[10]
Pointer portrait
https://en.wikipedia.org/wiki/Pointer_(dog_breed)#/media/File:Pointer_-_world_dog_show_2010.jpg
The pointer was developed in England over 300 years ago, and belongs to the breed of large sporting dogs. It has been mainly used for bird hunting, where the pointer directs the hunter to his prey, by facing in the direction of the game. The pointer was bred from crosses of greyhound, foxhound, spaniel, and bloodhound. It's between 58.4 and 66.4 cm tall and it's weight is normally between 22.7 and 27.2 kg.[11]
[1] Wharton, "Kerfol," 330
[2] "Pekingese." Encyclopædia Britannica. http://www.britannica.com/animal/Pekingese
[3] Haining, Peter, ed. The Demanding Dead. P.13
[4] Wharton, "Kerfol," 337.
[5] Wharton, "Kerfol," 337.
[6] "greyhound." The Columbia Encyclopedia, 6th ed.. 2015. Encyclopedia.com. http://www.encyclopedia.com/topic/greyhound.aspx#1
[7] Wharton, "Kerfol," 330.
[8] Wharton, "Kerfol," 338.
[9] "Sheepdog." Encyclopædia Britannica. http://www.britannica.com/animal/sheepdog
[10] Wharton, "Kerfol," 330.
[11] "pointer." The Columbia Encyclopedia, 6th ed.. 2015. Encyclopedia.com. http://www.encyclopedia.com/topic/pointer.aspx#1