If your voice is low and gruff, it's husky. A deep, gravelly voice is husky, and you're husky if you have a large, muscled, heavy body. You might even be a husky person with a husky voice.
When husky is a noun, it's a northern breed of dog that's bred to pull a sled. Your Alaskan Husky could have a husky bark, and your voice might be the result of a bad cold, or it just might be the normal way you speak. The husky that describes a voice comes from husk, in the sense of "dry as a husk." The husky dog's root is from 1850s Canadian English, hoskey, "Eskimo," or "Eskimo dog."