The native North Americans were introduced to the horse by Europeans.

[RhodriR]

Had they already domesticated the dog? Dogs had been domesticated in various parts of the world for thousands of years.

 

[RobRoy]

Horses existed in North America up until 8,000/10,00 years ago when they suddenly disappeared possibly because of hunting by humans.As you say they were reintroduced by Europeans around the 16th Century.
The dog as you no doubt know has been domesticated for thousands of years possibly descended from the gray wolf.