I've heard that the Native Americans greatly feared the dogs brought by the Spanish conquistadores because they did not have dogs themselves--they only had access to Chihuahua-like animals. But, given that the Inuit people DID have access to dogs, why did their use never travel south considering how incredibly useful they would have been.
Domestic dogs were present all over North and South America for thousands of years before the arrival of Europeans. This included a wide variety of dogs far beyond just Arctic sled-dogs and the little techichi of Mesoamerica. Most of these breeds have gone extinct or been absorbed into modern European breeds, so a lot of detail on Native American dogs has been lost, but there's still plenty of information in the archaeological, ethnographic, and early historic record.
In the American Southwest, dogs are amply represented in prehistoric rock art, pottery paintings, and deliberate burials. In some cases, dogs died a natural death and were buried with grave goods. In other cases, dogs were apparently sacrificed and buried in the floors of homes or religious structures, perhaps as a way of providing protection. Dog hair was spun into yarn and woven into cloth, and there's some evidence that Ancestral Puebloans bred dogs selectively for their fur.
Dogs were used as load-bearing animals throughout the North American Plains. In 1601, Spanish explorers of the Southern High Plains (Eastern New Mexico/West Texas), met a group of Apaches: "These Indians live in rancherias [small communities] which they move from place to place. They pack their huts, which are made of hides, on some small dogs." (1) When Native Americans later switched to horses pulling travois, they were continuing an ancient tradition of using dogs as draft animals.
There are countless other references to Native Americans using dogs as watchdogs, for hunting, draft animals, food, guard animals, and as pets, from all over North and South America. I'm more familiar with the Southwest so have focused on this region for examples. If you want more information on dogs in the Southwest, including some excellent illustrations, check out this 2008 Newsletter from the Center for Desert Archaeology (PDF Download).
The inuit would have a pack of huskies for sled dogs to travel during the cold winters, and build igloos for shelter during the winters.
Majority of the sled dogs were slaughtered by the rcmp and forced relocation of the inuit by the fed gov't and churches, sending a lot of inuit to residential schools or tuberculosis testing south.