The Ice Thief — Susan Gates

Gideon lives in the village with his cruel father and tries to earn a bit of money by stealing ice from the palace ponds, which he then sells to the palace cook. One day he is spotted by the guards and chased. He escapes into the palace where he hides in the room of the little Duchess. She lives as a prisoner, never allowed to play with 'common' children, and with only a mechanical duchess for company.

The little Duchess is eager to help Gideon escape - as long as she can run away with him, leaving the mechanical duchess in her place.