Where does the huntsman come from in the story of Snow White?

Yes, there is a Huntsman in the original tale:

Then [the queen] summoned a huntsman and said to him, "Take Snow-White out into the woods. I never want to see her again. Kill her, and as proof that she is dead bring her lungs and her liver back to me."

The huntsman obeyed and took Snow-White into the woods. He took out his hunting knife and was about to stab it into her innocent heart when she began to cry, saying, "Oh, dear huntsman, let me live. I will run into the wild woods and never come back."

Because she was so beautiful the huntsman took pity on her, and he said, "Run away, you poor child."

He thought, "The wild animals will soon devour you anyway," but still it was as if a stone had fallen from his heart, for he would not have to kill her.

Just then a young boar came running by. He killed it, cut out its lungs and liver, and took them back to the queen as proof of Snow-White's death.