Skijoring is a winter sport that involves a skier being pulled over snow/ice by a dog or horse.

Invented in Norway, skijoring is now enjoyed all over the world. Skijor (ski-jur) is a Norwegian word that means "ski-driving".

Dogs are the preferred method of locomotion. Often a single dog is used for short runs or races, while teams of dogs are employed for longer runs. A vehicle can been used to pull the skier, but this is generally considered unsafe and not recommended.

Equipment required:
A dog, preferably one trained for the purpose.
A dog sledding or other suitable harness for the dog(s).
A belt or climbing harness for the skier.
A tether line attaching the dog's harness and the skier, which should include a section of bungee material to reduce shock between the two.
Cross-country skis and poles.

Ideally, the dog should be trained to respond to commands such as GEE (turn left) and HAW (turn right) and WHOA (stop). Although most any dog will instinctively pull, some breeds are more adept and capable. Trained sled dogs will work best.

Most domestic pet dogs have been trained not to pull, so as not to dislocate the shoulder of their owner while taking a walk. Therefore, it can be very confusing for the animal if you attempt to use your household pet for a bit of skijoring in the park. Start slowly and make sure your dog understands when walkies ends and skijoring begins.

The sport is also known as ski-jor or ski-joring.

Sources
http://www.ptialaska.net/~skijor/
skiing.about.com/cs/nordicskiing/bb/ski-joring.htm